Question

question 22, 2.1.59
determine whether the statement is true or false.
13 ∉ {x | x ∈ n and x < 13}
choose the correct answer below.
○ a. false, because 13 is less than or equal to 13.
○ b. true, because 13 is not a natural number.
○ c. true, because 13 is a natural number, but is not less than 13.
○ d. false, because 13 is a natural number.

Explanation:

Step1: Analyze the set definition

The set is $\{x \mid x \in \mathbb{N} \text{ and } x < 13\}$, which includes all natural numbers strictly less than 13.

Step2: Evaluate 13's membership

Natural numbers $\mathbb{N}$ typically start at 1, and $13 < 13$ is false, so 13 is not in the set.

Step3: Match to correct option

The statement $13
otin \{x \mid x \in \mathbb{N} \text{ and } x < 13\}$ is true, which aligns with the reasoning that 13 is a natural number but not less than 13.

Answer:

C. True, because 13 is a natural number, but is not less than 13.