Prove that, for all sets $A$, $B$, and $C$, if $A cup B subseteq A cup C$, then $B subseteq C$.
$begingroup$
Apologize in advance for asking a question like this on this site, I have a final tomorrow, and there is no answer for this question so I have no other option but to ask. I need to know if this is True or False, and why.
elementary-set-theory
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
$endgroup$
add a comment |
$begingroup$
Apologize in advance for asking a question like this on this site, I have a final tomorrow, and there is no answer for this question so I have no other option but to ask. I need to know if this is True or False, and why.
elementary-set-theory
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
$endgroup$
$begingroup$
$A cup B$for example.
$endgroup$
– Randall
Dec 10 '18 at 4:52
$begingroup$
Please also accept the answer to your previous question.
$endgroup$
– Shaun
Dec 10 '18 at 5:09
add a comment |
$begingroup$
Apologize in advance for asking a question like this on this site, I have a final tomorrow, and there is no answer for this question so I have no other option but to ask. I need to know if this is True or False, and why.
elementary-set-theory
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
$endgroup$
Apologize in advance for asking a question like this on this site, I have a final tomorrow, and there is no answer for this question so I have no other option but to ask. I need to know if this is True or False, and why.
elementary-set-theory
elementary-set-theory
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
edited Dec 10 '18 at 4:56
eyeballfrog
6,103629
6,103629
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
asked Dec 10 '18 at 4:50
Gurnoor AujlaGurnoor Aujla
31
31
$begingroup$
$A cup B$for example.
$endgroup$
– Randall
Dec 10 '18 at 4:52
$begingroup$
Please also accept the answer to your previous question.
$endgroup$
– Shaun
Dec 10 '18 at 5:09
add a comment |
$begingroup$
$A cup B$for example.
$endgroup$
– Randall
Dec 10 '18 at 4:52
$begingroup$
Please also accept the answer to your previous question.
$endgroup$
– Shaun
Dec 10 '18 at 5:09
$begingroup$
$A cup B$ for example.$endgroup$
– Randall
Dec 10 '18 at 4:52
$begingroup$
$A cup B$ for example.$endgroup$
– Randall
Dec 10 '18 at 4:52
$begingroup$
Please also accept the answer to your previous question.
$endgroup$
– Shaun
Dec 10 '18 at 5:09
$begingroup$
Please also accept the answer to your previous question.
$endgroup$
– Shaun
Dec 10 '18 at 5:09
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Let $A=B={1}$ and $C=emptyset$ (i.e., the empty set).
The empty set is a great counterexample to a lot of would-be theorems, most of the time.
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
$endgroup$
add a comment |
$begingroup$
Not true in general.
For example, consider;
$$A={1,2,3,4,5}$$
$$B={1,2,3}$$ and $$C={1,2}$$
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
$endgroup$
add a comment |
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2 Answers
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2 Answers
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$begingroup$
Let $A=B={1}$ and $C=emptyset$ (i.e., the empty set).
The empty set is a great counterexample to a lot of would-be theorems, most of the time.
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
$endgroup$
add a comment |
$begingroup$
Let $A=B={1}$ and $C=emptyset$ (i.e., the empty set).
The empty set is a great counterexample to a lot of would-be theorems, most of the time.
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
$endgroup$
add a comment |
$begingroup$
Let $A=B={1}$ and $C=emptyset$ (i.e., the empty set).
The empty set is a great counterexample to a lot of would-be theorems, most of the time.
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
$endgroup$
Let $A=B={1}$ and $C=emptyset$ (i.e., the empty set).
The empty set is a great counterexample to a lot of would-be theorems, most of the time.
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
edited Dec 10 '18 at 5:03
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
answered Dec 10 '18 at 4:53
ShaunShaun
8,951113682
8,951113682
add a comment |
add a comment |
$begingroup$
Not true in general.
For example, consider;
$$A={1,2,3,4,5}$$
$$B={1,2,3}$$ and $$C={1,2}$$
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
$endgroup$
add a comment |
$begingroup$
Not true in general.
For example, consider;
$$A={1,2,3,4,5}$$
$$B={1,2,3}$$ and $$C={1,2}$$
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
$endgroup$
add a comment |
$begingroup$
Not true in general.
For example, consider;
$$A={1,2,3,4,5}$$
$$B={1,2,3}$$ and $$C={1,2}$$
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
$endgroup$
Not true in general.
For example, consider;
$$A={1,2,3,4,5}$$
$$B={1,2,3}$$ and $$C={1,2}$$
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
answered Dec 10 '18 at 5:13
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
41.5k42061
add a comment |
add a comment |
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$begingroup$
$A cup B$for example.$endgroup$
– Randall
Dec 10 '18 at 4:52
$begingroup$
Please also accept the answer to your previous question.
$endgroup$
– Shaun
Dec 10 '18 at 5:09