Consider the two finite sets and .

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

Problem

Consider the two finite sets

A = \{1,4\}

and

B = \{2,5,6\}

. (i) Define an ordered pair and distinguish it from an unordered pair by giving one example of each drawn from

A

and

B

. (ii) Explain, without direct enumeration, why every element of

A

can be paired with every element of

B

to form the Cartesian product

A \times B

. State the general counting principle involved. (iii) Use the reasoning in part (ii) to predict the total number of elements in

A \times B

. Then list all elements of

A \times B

explicitly and verify that your prediction is correct.