Question

(a) If A = {0, 2, 4, 6, 8} and B = {x : x is an even digit less than 5 and x ≥ 0}

Find (i) A ∪ B, (ii) B ∪ A, (iii) A ∩ B, (iv) B ∩ A

(b) If A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}

Verify (i) A ∪ B = B ∪ A, (ii) A ∩ B = B ∩ A

Answer 1

(a) A = {0, 2, 4, 6, 8}

B = {x: x is an even digit less than 5 and x ≥ 0} = {0, 2, 4}

(i) A ∪ B = {0, 2, 4, 6, 8} ∪ {0, 2, 4} = {0, 2, 4, 6, 8}

(ii) B ∪ A = {0, 2, 4} ∪ {2, 4, 6, 8} = {0, 2, 4, 6, 8}

(iii) A ∩ B = {0, 2, 4, 6, 8} ∩ {0, 2, 4} = {0, 2, 4}

(iv) B ∩ A = {0, 2, 4} ∩ {2, 4, 6, 8} = {0, 2, 4}

(b) A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}

(i) A ∪ B = {1, 2, 3, 4, 5} ∪ {2, 4, 6, 8} = {1, 2, 3, 4, 5, 6, 8}

B ∪ A = {2, 4, 6, 8} ∪ {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5, 6, 8}

∴ A ∪ B = B ∪ A

(ii) A ∩ B = {1, 2, 3, 4, 5} ∩ {2, 4, 6, 8} = {2, 4}

B ∩ A = {2, 4, 6, 8} ∩ {1, 2, 3, 4, 5} = {2, 4}

∴ A ∩ B = B ∩ A