If A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find

(i) A × (B ∩ C)

(ii) A × (B ∪ C)

Given: A = {x: x ∈W, x < 2} B = {x : x ∈N, 1 < x < 5} C = {3, 5} where W is the set of whole numbers

To find: (i) A × (B∩C) (ii) A × (B∪C)

Explanation: Given A = {x: x ∈W, x < 2}

This means set A contains all whole numbers which are less than 2, so

A = {0, 1}

And B = {x : x ∈N, 1 < x < 5}

This means set B contains all natural numbers which are greater than 1 and less than 5, so

B = {2, 3, 4}

(i) Now

(B∩C) is intersection of set B = {2, 3, 4} and set C = {3, 5} elements, so

(B∩C) = {3}

We need to find the Cartesian product of A = {0, 1} and (B∩C) = {3}

So,

A × (B∩C) = {(0, 3), (1, 3)}

This is the required Cartesian product.

(ii) Now

(B∪C) is union of set B = {2, 3, 4} and set C = {3, 5} elements, so

(B∪C) = {2, 3, 4, 5}

We need to find the Cartesian product of A = {0, 1} and (B∩C) = {2, 3, 4, 5}

So,

A × (B∪C) = {(0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 5)}

This is the required Cartesian product.