Prove that A∩(AUB)=A
Do I have have to show that A∩(AUB)⊂A and that A⊂A∩(AUB)????

Question

Prove that A∩(AUB)=A
Do I have have to show that  A∩(AUB)⊂A and that A⊂A∩(AUB)????

zarkon · Answer

if $A\subset C$ then $A\cap C=A$

anonymous · Answer

so I do.

anonymous · Answer

use venn diagram..much easier to prove sets identities

anonymous · Answer

it is sufficient to show that A ⊂(A∩(AUB)) and A∩(AUB) is a subset of A.
first we know that AUB will have all the elements of A, so that intersection of A and AUB will also contain all the elements in A, hence A is a subset of A∩(AUB). Now since AUB and intersection of it with A will only have elements of A (because if it contains elements which are not in A, then it will not be intersection of A and AUB lol.) so A∩(AUB) is a subset of A.
hence A∩(AUB)=A

anonymous · Answer

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