Let S Be the Set of Positive Integers $\in$

question 42

Essay

Let S be the set of positive integers defined by:
Basis step: 4 $\in$ S .
Recursive step: If n $\in$ S , then $5 n + 2 \in S$ and $5 n + 2 \in S$
(a) Show that if $n \in S$ , then $n \equiv 4$ (mod 6).
(b) Show that there exists an integer $m \equiv 4$ (mod 6) that does not belong to $S$

---

Definitions:

Physical Height

The measurement of an individual from the base to the top of their body when standing upright.

Popularity

The state of being widely admired, accepted, or sought after by a large number of people.

Unrepresentative

Describing a sample or subset that does not accurately reflect the characteristics of the larger population from which it's drawn.

Naturalistic Observation

A research method where subjects are observed in their natural environment without any manipulation by the observer.