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.)

Question

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.)

Quizplus · Accepted Answer

The Answer of 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.)

Define Sets AAA And BBB As Follows A={n∈Z∣n=8r−3A = \{ n \in \mathbf { Z } \mid n = 8 r - 3A={n∈Z∣n=8r−3

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