Question

Prove that A ∩ B ⊆B​

Answer 1

Answer:

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Step-by-step explanation:

I've learnt that in order to prove that X is a subset of Y, you have to show that if x is an element of X, x is also an element of Y. I am stuck on how to elegantly show that if x is an element of (A ∩ B), it is also an element of A.

This is what I have come up with until now:

x∈(A∩B)≡x∈A∧x∈B

For x∈A∧x∈B to be true, x∈A has to be true as well.

Therefore, x∈(A∩B)⟹x∈A