Let and let . Consider the Cartesian product . Assume the ordered pairs are arranged…

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

A = \{0, 1, 2\}

and let

B = \{ n \in \mathbb{N} \mid n \ge 5 \}

. Consider the Cartesian product

A \times B

. Assume the ordered pairs are arranged in lexicographic (dictionary) order, i.e., firstly by the element of

A

(in increasing order) and, within each fixed first component, by the element of

B

(in increasing order). (i) List the first nine ordered pairs of

A \times B

in this order. (ii) Identify the 12th ordered pair in the same order. (iii) State whether

A \times B

is finite or infinite, and give a brief justification based on the definitions involved.