A={x ∈ ℤ | x ≡ 7 (mod 8)} B={x ∈ ℤ | x ≡ 3 (mod 4)} Is A ⊆ B? Yes Since x ∈ A, then x = 7 + 8a = 8a + 7 = 4(2a) + 4 + 3 = 4(2a + 1) + 3. And since the ∈ B are of the form x = 3 + 4b = 4b + 3, all x = 4p + 3 and A ⊆ B. Q.E.D. Correct?
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Yes, it seems correct.
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