If $A subseteq B$ then $A times C subseteq B times C$ [closed]
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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
closed as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen Sep 11 at 3:05
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." â Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
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up vote
1
down vote
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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
closed as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen Sep 11 at 3:05
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." â Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
I'm very new to formal proofs and set theory!
â rickyrichboy
Aug 31 at 3:30
Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
â copper.hat
Aug 31 at 3:34
What does it mean for a point $(a,c)$ to be in $A times C$?
â Yagger
Aug 31 at 3:43
add a comment |Â
up vote
1
down vote
favorite
up vote
1
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
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
edited Sep 9 at 10:26
Jendrik Stelzner
7,69121137
7,69121137
asked Aug 31 at 3:27
rickyrichboy
274
274
closed as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen Sep 11 at 3:05
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." â Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
closed as off-topic by Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen Sep 11 at 3:05
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." â Did, Jendrik Stelzner, Holo, NCh, Jyrki Lahtonen
I'm very new to formal proofs and set theory!
â rickyrichboy
Aug 31 at 3:30
Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
â copper.hat
Aug 31 at 3:34
What does it mean for a point $(a,c)$ to be in $A times C$?
â Yagger
Aug 31 at 3:43
add a comment |Â
I'm very new to formal proofs and set theory!
â rickyrichboy
Aug 31 at 3:30
Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
â copper.hat
Aug 31 at 3:34
What does it mean for a point $(a,c)$ to be in $A times C$?
â Yagger
Aug 31 at 3:43
I'm very new to formal proofs and set theory!
â rickyrichboy
Aug 31 at 3:30
I'm very new to formal proofs and set theory!
â rickyrichboy
Aug 31 at 3:30
Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
â copper.hat
Aug 31 at 3:34
Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
â copper.hat
Aug 31 at 3:34
What does it mean for a point $(a,c)$ to be in $A times C$?
â Yagger
Aug 31 at 3:43
What does it mean for a point $(a,c)$ to be in $A times C$?
â Yagger
Aug 31 at 3:43
add a comment |Â
1 Answer
1
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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 $xin Btimes C$.
@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.
â vadim123
Aug 31 at 13:17
add a comment |Â
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 $xin Btimes C$.
@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.
â vadim123
Aug 31 at 13:17
add a comment |Â
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 $xin Btimes C$.
@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.
â vadim123
Aug 31 at 13:17
add a comment |Â
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 $xin Btimes C$.
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 $xin Btimes C$.
answered Aug 31 at 3:33
vadim123
74.6k896186
74.6k896186
@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.
â vadim123
Aug 31 at 13:17
add a comment |Â
@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.
â 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.
â 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.
â vadim123
Aug 31 at 13:17
add a comment |Â
I'm very new to formal proofs and set theory!
â rickyrichboy
Aug 31 at 3:30
Pick a point $(a,c) in A times C$. Then show that $(a,c) in B times C$.
â copper.hat
Aug 31 at 3:34
What does it mean for a point $(a,c)$ to be in $A times C$?
â Yagger
Aug 31 at 3:43