Answer :

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


To find: (PQ) × (PQ)


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


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


(PQ) = {0, 1, 2}


And,


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


(PQ) = {1, 2}


We need to find the Cartesian product of (PQ) = {0, 1, 2} and (PQ) = {1, 2}


So,


(PQ) × (PQ) = {(0, 1), (0, 2), (1, 1), (1, 2), (2, 1), (2, 2)}


This is the required Cartesian product.


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