Question

The empty set is the special set that contains no (i.e., zero) elements in the set. We use the notation empty set to represent the empty set. Let U be the universal set, and let A be a set of elements chosen from U. What is the value of empty set space x space A ?

Answer 1

The value of a Cartesian product between an empty set and set A is equal to the empty set.

Explanation:

The cartesian product is given by:

A×B= {(a,b): a∈A, b∈B}

This means that each element of set A is combined with an element of set B.

The empty set is the unique set having no elements and its size is zero.

Let Ф be the empty set and let A be a set of elements chosen from U.

A×Ф=Ф

Since the empty set has no elements, no ordered pairs can be formed and the result is the empty set.