Question: For sets H and K, we define the intersection H K by H K = {x |x H and x K}.

For sets H and K, we define the intersection H ∩ K by H ∩ K = {x |x ∈ H and x ∈ K}. Show that if H ≤ G and K ≤ G, then H ∩ K ≤G. (Remember: ≤ denotes "is a subgroup of," not "is a subset of.")

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