Let $X = \{ l \in \mathrm { Z } \mid l = 5 a + 2$

question 4

Essay

Let $X = \{ l \in \mathrm { Z } \mid l = 5 a + 2$ for some integer $a \} , Y = \{ m \in \mathrm { Z } \mid m = 4 b + 3$ for some integer $b \}$ , and $Z = \{ n \in \mathrm { Z } \mid n = 4 c - 1$ for some integer $c \}$ .
(a) Is $X \subseteq Y$ ?
(b) Is $Y \subseteq Z$ ?
Justify your answers carefully. (In other words, provide a proof if the statement is true or a disproof if the statement is false.)