**Cartesian Product of Sets Worksheet :**

Here we are going to see some practice problems on Cartesian product of sets.

(1) Find A x B , A x A and B x A

(i) A = {2, −2, 3} and B = {1, −4}

(ii) A = B = {p, q}

(iii) A = {m, n} ; B = ∅ Solution

(2) Let A = {1, 2, 3} and B = {x | x is a prime number less than 10}. Find A x B and B x A. Solution

(3) If B × A = {(−2, 3),(−2, 4),(0, 3),(0, 4),(3, 3),(3, 4)} find A and B. Solution

(4) If A = {5, 6} , B = {4, 5, 6} , C = {5, 6, 7} , Show that A × A = (B × B) n (C × C). Solution

(5) Given A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4} and D = {1, 3, 5}, check if (A n C) × (B n D) = (A × B)n(C × D) is true? Solution

(6) Let A = {x ∈ W | x < 2} , B = {x ∈|1 < x ≤ 4} and C = {3, 5} . Verify that

(i) A × (B U C) = (A × B) U (A × C)

(ii) A × (B n C) = (A × B) n (A × C)

(iii) (A U B) × C = (A × C) U (B × C) Solution

(7) Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that

(i) (A n B) × C = (A × C) n (B × C)

(ii) A × (B −C) = (A × B) − (A × C) Solution

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