If P = {x : x < 3, x ∈ N}, Q = {x : x ≤ 2, x ∈ W}. Find (P ∪ Q) × (P ∩ Q), where W is the set of whole numbers.

Given: P = {x: x < 3, x ∈N}, Q = {x : x ≤ 2, x ∈W} where W is the set of whole numbers

To find: (P∪Q) × (P∩Q)

Explanation: Given P = {x: x < 3, x ∈N}

This means set P contains all natural numbers which are less than 3, so

P = {1, 2}

And Q = {x : x ≤ 2, x ∈W}

This means set Q contains all whole numbers which are less than or equal to 2, so

Q = {0, 1, 2}

Now

(P∪Q) is union of set P = {1, 2} and set Q = {0, 1, 2} elements, so

(P∪Q) = {0, 1, 2}

And,

(P∩Q) is intersection of set P = {1, 2} and set Q = {0, 1, 2} elements, so

(P∩Q) = {1, 2}

We need to find the Cartesian product of (P∪Q) = {0, 1, 2} and (P∩Q) = {1, 2}

So,

(P∪Q) × (P∩Q) = {(0, 1), (0, 2), (1, 1), (1, 2), (2, 1), (2, 2)}

This is the required Cartesian product.