Prove that, for all sets $A$, $B$, and $C$, if $A cup B subseteq A cup C$, then $B subseteq C$.
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
6,058629
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
add a comment |
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
6,058629
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
$A cup B$for example.
– Randall
Dec 10 '18 at 4:52
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark $checkmark$ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, What should I do if someone answers my question?.
– Shaun
Dec 10 '18 at 5:04
Please also accept the answer to your previous question.
– Shaun
Dec 10 '18 at 5:09
add a comment |
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
6,058629
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
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
6,058629
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
edited Dec 10 '18 at 4:56
eyeballfrog
6,058629
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
edited Dec 10 '18 at 4:56
eyeballfrog
6,058629
edited Dec 10 '18 at 4:56
eyeballfrog
6,058629
edited Dec 10 '18 at 4:56
eyeballfrog
6,058629
6,058629
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
asked Dec 10 '18 at 4:50
Gurnoor Aujla
31
31
$A cup B$for example.
– Randall
Dec 10 '18 at 4:52
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark $checkmark$ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, What should I do if someone answers my question?.
– Shaun
Dec 10 '18 at 5:04
Please also accept the answer to your previous question.
– Shaun
Dec 10 '18 at 5:09
add a comment |
$A cup B$for example.
– Randall
Dec 10 '18 at 4:52
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark $checkmark$ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, What should I do if someone answers my question?.
– Shaun
Dec 10 '18 at 5:04
Please also accept the answer to your previous question.
– Shaun
Dec 10 '18 at 5:09
$A cup B$ for example.– Randall
Dec 10 '18 at 4:52
$A cup B$ for example.– Randall
Dec 10 '18 at 4:52
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark $checkmark$ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, What should I do if someone answers my question?.
– Shaun
Dec 10 '18 at 5:04
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark $checkmark$ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, What should I do if someone answers my question?.
– Shaun
Dec 10 '18 at 5:04
Please also accept the answer to your previous question.
– Shaun
Dec 10 '18 at 5:09
Please also accept the answer to your previous question.
– Shaun
Dec 10 '18 at 5:09
add a comment |
2 Answers
2
active
oldest
votes
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
Shaun
8,760113680
add a comment |
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-Kermani
40.9k42059
add a comment |
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2 Answers
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2 Answers
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active
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votes
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
Shaun
8,760113680
add a comment |
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
Shaun
8,760113680
add a comment |
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
Shaun
8,760113680
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
Shaun
8,760113680
edited Dec 10 '18 at 5:03
answered Dec 10 '18 at 4:53
Shaun
8,760113680
answered Dec 10 '18 at 4:53
Shaun
8,760113680
answered Dec 10 '18 at 4:53
Shaun
8,760113680
8,760113680
add a comment |
add a comment |
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-Kermani
40.9k42059
add a comment |
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-Kermani
40.9k42059
add a comment |
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-Kermani
40.9k42059
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-Kermani
40.9k42059
answered Dec 10 '18 at 5:13
Mohammad Riazi-Kermani
40.9k42059
answered Dec 10 '18 at 5:13
Mohammad Riazi-Kermani
40.9k42059
answered Dec 10 '18 at 5:13
Mohammad Riazi-Kermani
40.9k42059
40.9k42059
add a comment |
add a comment |
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$A cup B$for example.– Randall
Dec 10 '18 at 4:52
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark $checkmark$ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, What should I do if someone answers my question?.
– Shaun
Dec 10 '18 at 5:04
Please also accept the answer to your previous question.
– Shaun
Dec 10 '18 at 5:09