Define Sets $A$ And $B$ As Follows $A = \{ n \in \mathbf { Z } \mid n = 8 r - 3$

question 13

Essay

Define sets $A$ and $B$ as follows: $A = \{ n \in \mathbf { Z } \mid n = 8 r - 3$ for some integer $r \}$ and $B = \{ m \in \mathbf { Z } \mid m = 4 s + 1$ for some integer $s \}$ .
(a) Is $A \subseteq B$ ?
(b) Is $B \subseteq A$ ?
Justify your answers carefully. (In other words, provide a proof if the statement is true or a disproof if the statement is false.)

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