Assume $A subset B$ and $A neq emptyset$. Prove $B neq emptyset$.
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I have an exercise stating
Assume $A subset B$ and $A neq emptyset$. Prove $B neq emptyset$.
Is my proof adequate, or have I missed anything out? Any tips would be greatly appreciated as I am self taught new to proof writing.
Proof : As $A neq emptyset$ , $ exists a , (a in A)$. Also, as $A subset B$ , $forall a in A, (a in B)$. From this we get $exists a , (a in B)$. Therefore, $B neq emptyset$
elementary-set-theory proof-verification proof-writing
add a comment |Â
up vote
2
down vote
favorite
I have an exercise stating
Assume $A subset B$ and $A neq emptyset$. Prove $B neq emptyset$.
Is my proof adequate, or have I missed anything out? Any tips would be greatly appreciated as I am self taught new to proof writing.
Proof : As $A neq emptyset$ , $ exists a , (a in A)$. Also, as $A subset B$ , $forall a in A, (a in B)$. From this we get $exists a , (a in B)$. Therefore, $B neq emptyset$
elementary-set-theory proof-verification proof-writing
1
yeah that's right
â Akababa
Aug 7 at 14:57
@Akababa Thank you
â Ewan Miller
Aug 7 at 14:59
Your proof is perfectly correct !
â Pjonin
Aug 7 at 14:59
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I have an exercise stating
Assume $A subset B$ and $A neq emptyset$. Prove $B neq emptyset$.
Is my proof adequate, or have I missed anything out? Any tips would be greatly appreciated as I am self taught new to proof writing.
Proof : As $A neq emptyset$ , $ exists a , (a in A)$. Also, as $A subset B$ , $forall a in A, (a in B)$. From this we get $exists a , (a in B)$. Therefore, $B neq emptyset$
elementary-set-theory proof-verification proof-writing
I have an exercise stating
Assume $A subset B$ and $A neq emptyset$. Prove $B neq emptyset$.
Is my proof adequate, or have I missed anything out? Any tips would be greatly appreciated as I am self taught new to proof writing.
Proof : As $A neq emptyset$ , $ exists a , (a in A)$. Also, as $A subset B$ , $forall a in A, (a in B)$. From this we get $exists a , (a in B)$. Therefore, $B neq emptyset$
elementary-set-theory proof-verification proof-writing
asked Aug 7 at 14:56
Ewan Miller
12612
12612
1
yeah that's right
â Akababa
Aug 7 at 14:57
@Akababa Thank you
â Ewan Miller
Aug 7 at 14:59
Your proof is perfectly correct !
â Pjonin
Aug 7 at 14:59
add a comment |Â
1
yeah that's right
â Akababa
Aug 7 at 14:57
@Akababa Thank you
â Ewan Miller
Aug 7 at 14:59
Your proof is perfectly correct !
â Pjonin
Aug 7 at 14:59
1
1
yeah that's right
â Akababa
Aug 7 at 14:57
yeah that's right
â Akababa
Aug 7 at 14:57
@Akababa Thank you
â Ewan Miller
Aug 7 at 14:59
@Akababa Thank you
â Ewan Miller
Aug 7 at 14:59
Your proof is perfectly correct !
â Pjonin
Aug 7 at 14:59
Your proof is perfectly correct !
â Pjonin
Aug 7 at 14:59
add a comment |Â
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1
yeah that's right
â Akababa
Aug 7 at 14:57
@Akababa Thank you
â Ewan Miller
Aug 7 at 14:59
Your proof is perfectly correct !
â Pjonin
Aug 7 at 14:59