Is a $S$ an element or subset or both of $T$? [closed]
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I have a question on basic set theory.
$S = a, b$
$T= a, b, c, d, e, f $
- Is $S$ a subset of $T$?
- Is $S$ an element of $T$?
elementary-set-theory
closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
 |Â
show 5 more comments
up vote
-2
down vote
favorite
I have a question on basic set theory.
$S = a, b$
$T= a, b, c, d, e, f $
- Is $S$ a subset of $T$?
- Is $S$ an element of $T$?
elementary-set-theory
closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32
I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36
1
Did you though?
– Asaf Karagila
Aug 1 at 11:38
1
Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42
 |Â
show 5 more comments
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
I have a question on basic set theory.
$S = a, b$
$T= a, b, c, d, e, f $
- Is $S$ a subset of $T$?
- Is $S$ an element of $T$?
elementary-set-theory
I have a question on basic set theory.
$S = a, b$
$T= a, b, c, d, e, f $
- Is $S$ a subset of $T$?
- Is $S$ an element of $T$?
elementary-set-theory
edited Aug 1 at 11:48
Asaf Karagila
291k31401731
291k31401731
asked Aug 1 at 11:29
user580935
closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32
I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36
1
Did you though?
– Asaf Karagila
Aug 1 at 11:38
1
Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42
 |Â
show 5 more comments
$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32
I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36
1
Did you though?
– Asaf Karagila
Aug 1 at 11:38
1
Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42
$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31
$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32
I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36
I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36
1
1
Did you though?
– Asaf Karagila
Aug 1 at 11:38
Did you though?
– Asaf Karagila
Aug 1 at 11:38
1
1
Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42
Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42
 |Â
show 5 more comments
4 Answers
4
active
oldest
votes
up vote
1
down vote
accepted
The easy way to solve these questions is to put dummy variables.
This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.
Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?
add a comment |Â
up vote
1
down vote
$S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.
$S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.
2
This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
– Henning Makholm
Aug 1 at 11:46
add a comment |Â
up vote
0
down vote
No and no, because $a neq a$ and $b neq b$.
To (i): It is
$$a, b subset T,$$
but
$$a, b notsubset T.$$
To (ii): It is
$$a in T text and b in T, $$
but
$$ a,b notin T. $$
add a comment |Â
up vote
0
down vote
Edit : Since the question had two different versions, I'm gonna reply to both.
Case where $S = a,b$ :
$S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.
Case where $S = a,b$ :
$S$ is a subset of $T$ since all elements of $S$ are elements of $T$.
$S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.
2
"Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
– Henning Makholm
Aug 1 at 11:43
But doesn't my example in parenthesis resolves the ambiguity ?
– Pakos
Aug 1 at 11:56
add a comment |Â
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
The easy way to solve these questions is to put dummy variables.
This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.
Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?
add a comment |Â
up vote
1
down vote
accepted
The easy way to solve these questions is to put dummy variables.
This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.
Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
The easy way to solve these questions is to put dummy variables.
This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.
Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?
The easy way to solve these questions is to put dummy variables.
This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.
Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?
answered Aug 1 at 11:46
Asaf Karagila
291k31401731
291k31401731
add a comment |Â
add a comment |Â
up vote
1
down vote
$S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.
$S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.
2
This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
– Henning Makholm
Aug 1 at 11:46
add a comment |Â
up vote
1
down vote
$S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.
$S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.
2
This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
– Henning Makholm
Aug 1 at 11:46
add a comment |Â
up vote
1
down vote
up vote
1
down vote
$S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.
$S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.
$S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.
$S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.
answered Aug 1 at 11:41


Fred
37k1237
37k1237
2
This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
– Henning Makholm
Aug 1 at 11:46
add a comment |Â
2
This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
– Henning Makholm
Aug 1 at 11:46
2
2
This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
– Henning Makholm
Aug 1 at 11:46
This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
– Henning Makholm
Aug 1 at 11:46
add a comment |Â
up vote
0
down vote
No and no, because $a neq a$ and $b neq b$.
To (i): It is
$$a, b subset T,$$
but
$$a, b notsubset T.$$
To (ii): It is
$$a in T text and b in T, $$
but
$$ a,b notin T. $$
add a comment |Â
up vote
0
down vote
No and no, because $a neq a$ and $b neq b$.
To (i): It is
$$a, b subset T,$$
but
$$a, b notsubset T.$$
To (ii): It is
$$a in T text and b in T, $$
but
$$ a,b notin T. $$
add a comment |Â
up vote
0
down vote
up vote
0
down vote
No and no, because $a neq a$ and $b neq b$.
To (i): It is
$$a, b subset T,$$
but
$$a, b notsubset T.$$
To (ii): It is
$$a in T text and b in T, $$
but
$$ a,b notin T. $$
No and no, because $a neq a$ and $b neq b$.
To (i): It is
$$a, b subset T,$$
but
$$a, b notsubset T.$$
To (ii): It is
$$a in T text and b in T, $$
but
$$ a,b notin T. $$
answered Aug 1 at 11:46


til
694
694
add a comment |Â
add a comment |Â
up vote
0
down vote
Edit : Since the question had two different versions, I'm gonna reply to both.
Case where $S = a,b$ :
$S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.
Case where $S = a,b$ :
$S$ is a subset of $T$ since all elements of $S$ are elements of $T$.
$S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.
2
"Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
– Henning Makholm
Aug 1 at 11:43
But doesn't my example in parenthesis resolves the ambiguity ?
– Pakos
Aug 1 at 11:56
add a comment |Â
up vote
0
down vote
Edit : Since the question had two different versions, I'm gonna reply to both.
Case where $S = a,b$ :
$S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.
Case where $S = a,b$ :
$S$ is a subset of $T$ since all elements of $S$ are elements of $T$.
$S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.
2
"Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
– Henning Makholm
Aug 1 at 11:43
But doesn't my example in parenthesis resolves the ambiguity ?
– Pakos
Aug 1 at 11:56
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Edit : Since the question had two different versions, I'm gonna reply to both.
Case where $S = a,b$ :
$S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.
Case where $S = a,b$ :
$S$ is a subset of $T$ since all elements of $S$ are elements of $T$.
$S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.
Edit : Since the question had two different versions, I'm gonna reply to both.
Case where $S = a,b$ :
$S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.
Case where $S = a,b$ :
$S$ is a subset of $T$ since all elements of $S$ are elements of $T$.
$S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.
edited Aug 1 at 11:54
answered Aug 1 at 11:39
Pakos
11
11
2
"Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
– Henning Makholm
Aug 1 at 11:43
But doesn't my example in parenthesis resolves the ambiguity ?
– Pakos
Aug 1 at 11:56
add a comment |Â
2
"Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
– Henning Makholm
Aug 1 at 11:43
But doesn't my example in parenthesis resolves the ambiguity ?
– Pakos
Aug 1 at 11:56
2
2
"Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
– Henning Makholm
Aug 1 at 11:43
"Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
– Henning Makholm
Aug 1 at 11:43
But doesn't my example in parenthesis resolves the ambiguity ?
– Pakos
Aug 1 at 11:56
But doesn't my example in parenthesis resolves the ambiguity ?
– Pakos
Aug 1 at 11:56
add a comment |Â
$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32
I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36
1
Did you though?
– Asaf Karagila
Aug 1 at 11:38
1
Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42