- #1

- 699

- 5

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?