Question

determine whether the following statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. \\{x|x∈n and 75 < x < 105\\} ⊆ \\{x|x∈n and 75 ≤ x ≤ 105\\} select the correct choice below and, if necessary, fill in the answer box within your choice. a. the statement is true. b. the statement is false. \\{x|x∈n and 75 < x < 105\\} \\{x|x∈n and 75 ≤ x ≤ 105\\} is true.

Explanation:

Step1: Define set membership

Let \( A = \{x|x\in\mathbb{N} \text{ and } 75 < x < 105\} \), \( B = \{x|x\in\mathbb{N} \text{ and } 75 \leq x \leq 105\} \)

Step2: Analyze subset condition

A set \( A \subseteq B \) if every element of \( A \) is in \( B \). All natural numbers \( x \) where \( 75 < x < 105 \) are also in the range \( 75 \leq x \leq 105 \), since the latter includes 75, 105, and all numbers in between.

Answer:

A. The statement is true.