If $A subseteq B$ then $A times C subseteq B times C$ [on hold]

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Prove that if $A subseteq B$ then $A times C subseteq B times C$




I don't even know where to start here, can somebody at least point me in the right direction?






elementary-set-theory







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put on hold as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen 2 days ago


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." – Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.












  • I'm very new to formal proofs and set theory!
    – rickyrichboy
    Aug 31 at 3:30










  • Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
    – copper.hat
    Aug 31 at 3:34










  • What does it mean for a point $(a,c)$ to be in $A times C$?
    – Yagger
    Aug 31 at 3:43















up vote
2
down vote

favorite













Prove that if $A subseteq B$ then $A times C subseteq B times C$




I don't even know where to start here, can somebody at least point me in the right direction?






elementary-set-theory







share|cite|improve this question















put on hold as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen 2 days ago


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." – Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.












  • I'm very new to formal proofs and set theory!
    – rickyrichboy
    Aug 31 at 3:30










  • Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
    – copper.hat
    Aug 31 at 3:34










  • What does it mean for a point $(a,c)$ to be in $A times C$?
    – Yagger
    Aug 31 at 3:43













up vote
2
down vote

favorite









up vote
2
down vote

favorite












Prove that if $A subseteq B$ then $A times C subseteq B times C$




I don't even know where to start here, can somebody at least point me in the right direction?






elementary-set-theory







share|cite|improve this question
















Prove that if $A subseteq B$ then $A times C subseteq B times C$




I don't even know where to start here, can somebody at least point me in the right direction?






elementary-set-theory




elementary-set-theory






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 9 at 10:26









Jendrik Stelzner

7,69121137




7,69121137










asked Aug 31 at 3:27









rickyrichboy

273




273




put on hold as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen 2 days ago


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." – Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen 2 days ago


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." – Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.











  • I'm very new to formal proofs and set theory!
    – rickyrichboy
    Aug 31 at 3:30










  • Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
    – copper.hat
    Aug 31 at 3:34










  • What does it mean for a point $(a,c)$ to be in $A times C$?
    – Yagger
    Aug 31 at 3:43

















  • I'm very new to formal proofs and set theory!
    – rickyrichboy
    Aug 31 at 3:30










  • Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
    – copper.hat
    Aug 31 at 3:34










  • What does it mean for a point $(a,c)$ to be in $A times C$?
    – Yagger
    Aug 31 at 3:43
















I'm very new to formal proofs and set theory!
– rickyrichboy
Aug 31 at 3:30




I'm very new to formal proofs and set theory!
– rickyrichboy
Aug 31 at 3:30












Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
– copper.hat
Aug 31 at 3:34




Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
– copper.hat
Aug 31 at 3:34












What does it mean for a point $(a,c)$ to be in $A times C$?
– Yagger
Aug 31 at 3:43





What does it mean for a point $(a,c)$ to be in $A times C$?
– Yagger
Aug 31 at 3:43











1 Answer
1






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oldest

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up vote
3
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accepted










Step 1. Let $xin Atimes C$ be arbitrary.



Step 2. This means that $x=(u,v)$ where $uin A$ and $vin C$.



Step 3. Since $Asubseteq B$, in fact, $uin B$.



Step 4. Hence $xin Btimes C$.






share|cite|improve this answer




















  • @KaviRamaMurthy, you are incorrect. If $C$ is empty, then $Atimes C=Btimes C=emptyset$. The statement is vacuously true, and the proof also holds vacuously.
    – vadim123
    Aug 31 at 13:17

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
3
down vote



accepted










Step 1. Let $xin Atimes C$ be arbitrary.



Step 2. This means that $x=(u,v)$ where $uin A$ and $vin C$.



Step 3. Since $Asubseteq B$, in fact, $uin B$.



Step 4. Hence $xin Btimes C$.






share|cite|improve this answer




















  • @KaviRamaMurthy, you are incorrect. If $C$ is empty, then $Atimes C=Btimes C=emptyset$. The statement is vacuously true, and the proof also holds vacuously.
    – vadim123
    Aug 31 at 13:17














up vote
3
down vote



accepted










Step 1. Let $xin Atimes C$ be arbitrary.



Step 2. This means that $x=(u,v)$ where $uin A$ and $vin C$.



Step 3. Since $Asubseteq B$, in fact, $uin B$.



Step 4. Hence $xin Btimes C$.






share|cite|improve this answer




















  • @KaviRamaMurthy, you are incorrect. If $C$ is empty, then $Atimes C=Btimes C=emptyset$. The statement is vacuously true, and the proof also holds vacuously.
    – vadim123
    Aug 31 at 13:17












up vote
3
down vote



accepted







up vote
3
down vote



accepted






Step 1. Let $xin Atimes C$ be arbitrary.



Step 2. This means that $x=(u,v)$ where $uin A$ and $vin C$.



Step 3. Since $Asubseteq B$, in fact, $uin B$.



Step 4. Hence $xin Btimes C$.






share|cite|improve this answer












Step 1. Let $xin Atimes C$ be arbitrary.



Step 2. This means that $x=(u,v)$ where $uin A$ and $vin C$.



Step 3. Since $Asubseteq B$, in fact, $uin B$.



Step 4. Hence $xin Btimes C$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 31 at 3:33









vadim123

74.3k895185




74.3k895185











  • @KaviRamaMurthy, you are incorrect. If $C$ is empty, then $Atimes C=Btimes C=emptyset$. The statement is vacuously true, and the proof also holds vacuously.
    – vadim123
    Aug 31 at 13:17
















  • @KaviRamaMurthy, you are incorrect. If $C$ is empty, then $Atimes C=Btimes C=emptyset$. The statement is vacuously true, and the proof also holds vacuously.
    – vadim123
    Aug 31 at 13:17















@KaviRamaMurthy, you are incorrect. If $C$ is empty, then $Atimes C=Btimes C=emptyset$. The statement is vacuously true, and the proof also holds vacuously.
– vadim123
Aug 31 at 13:17




@KaviRamaMurthy, you are incorrect. If $C$ is empty, then $Atimes C=Btimes C=emptyset$. The statement is vacuously true, and the proof also holds vacuously.
– vadim123
Aug 31 at 13:17


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