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, $B neq emptyset$







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  • 1




    yeah that's right
    – Akababa
    Aug 7 at 14:57










  • @Akababa Thank you
    – Ewan Miller
    Aug 7 at 14:59










  • Your proof is perfectly correct !
    – Pjonin
    Aug 7 at 14:59














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, $B neq emptyset$







share|cite|improve this question















  • 1




    yeah that's right
    – Akababa
    Aug 7 at 14:57










  • @Akababa Thank you
    – Ewan Miller
    Aug 7 at 14:59










  • Your proof is perfectly correct !
    – Pjonin
    Aug 7 at 14:59












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, $B neq emptyset$







share|cite|improve this question











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, $B neq emptyset$









share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 7 at 14:56









Ewan Miller

12612




12612







  • 1




    yeah that's right
    – Akababa
    Aug 7 at 14:57










  • @Akababa Thank you
    – Ewan Miller
    Aug 7 at 14:59










  • Your proof is perfectly correct !
    – Pjonin
    Aug 7 at 14:59












  • 1




    yeah that's right
    – Akababa
    Aug 7 at 14:57










  • @Akababa Thank you
    – Ewan Miller
    Aug 7 at 14:59










  • Your proof is perfectly correct !
    – Pjonin
    Aug 7 at 14:59







1




1




yeah that's right
– Akababa
Aug 7 at 14:57




yeah that's right
– Akababa
Aug 7 at 14:57












@Akababa Thank you
– Ewan Miller
Aug 7 at 14:59




@Akababa Thank you
– Ewan Miller
Aug 7 at 14:59












Your proof is perfectly correct !
– Pjonin
Aug 7 at 14:59




Your proof is perfectly correct !
– Pjonin
Aug 7 at 14:59















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