A={x ∈ ℤ | x ≡ 7 (mod 8)}(adsbygoogle = window.adsbygoogle || []).push({});

B={x ∈ ℤ | x ≡ 3 (mod 4)}

Is A ⊆ B? Yes

Since x ∈ A, then x_{a}= 7 + 8a = 8a + 7 = 2(4a + 3) +1. And since the ∈ B are of the form x_{b}= 3 + 4b = 4b + 3 = 2(2b + 1) + 1, both ∈ A,B are odd. A ⊆ B since the ∈ of both sets are of 2p + 1. Q.E.D.

Is this correct?

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# Homework Help: Sets: Is A ⊆ B? A={x ∈ ℤ | x ≡ 7 (mod 8)} B={x ∈ ℤ | x ≡ 3 (mod 4)}

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