volume_mute

Product with empty set

publish date: 2022/08/24 08:47:00 GMT+10

volume_mute

Let A = {1, 2, 3}, B = ∅, Then A x B = 

{(1,1), (2,2), (3,3)}
∅
{1, 2, 3}
{(1,∅),(2,∅),(3,∅)}

Correct Answer

∅

Explanation

A x B is not defined as a set of ordered pairs if either A or B is empty. However, A x {∅} = {(1, ∅), (2, ∅), (3, ∅)}. But this set of ordered pairs is of no use to us.

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

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