Let $A = \{x \in \mathbb{N} \mid 1 \le x \le 12 \text{ and } x \text{ is a multiple of } 3\}$ …

Mathematics

Problem

Let

A = \{x \in \mathbb{N} \mid 1 \le x \le 12 \text{ and } x \text{ is a multiple of } 3\}

, and let

B

be the set of distinct letters appearing in the word “MATHS”. a. (i) List the elements of

A

and

B

. b. (ii) Find the number of ordered pairs in the Cartesian product

A \times B

. c. (iii) Determine the number of ordered pairs

(a,b)

A \times B

for which

a > 6