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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Definitions:

MSA

An abbreviation for Metropolitan Statistical Area, which is a geographical region with a relatively high population density at its core and close economic ties throughout the area.

Critical Value

A point on the scale of a test statistic beyond which the null hypothesis is rejected in favor of an alternative hypothesis.

Interaction Effect

A statistical phenomenon where the effect of one independent variable on a dependent variable depends on the level of another independent variable.

DfB

Degrees of Freedom Between groups, referring to the number of independent values in the calculation of variance between the different groups under study.