Question

If A = {a, b, c, d}, B = {p, q, r} and C = {a, b, p, q}, then examine the validity of the following: 

(i) A – B = C 

(ii) B – C ≠ A 

(iii) B – A = Φ 

(iv) (A ∪ B) – C = {c, d, r} 

(v) (A ∪ B) ∩ C = C

Answer 1

Given, 

A = {a, b, c, d}, B = {p, q, r}, C = {a, b, p, q} 

(i) (A – B) = C 

L.H.S. = A – B = {a, b, c, d} – {p, q, r} = {a, b, c, d}

⇒ A – B ≠ C (False) 

(ii) B – C ≠ A 

B – C = {p, q, r,} – {a, b, p, q} = {r} ≠ A (True) 

(iii) B – A = Φ 

B – A = {p, q, r,} – {a, b, c, d} 

= {p, q, r} ≠ Φ (False) 

(iv) (A ∪ B) – C 

A ∪ B = {a, b, c, d} ∪ {p, q, r} = {a, b, c, d, p, q, r} 

(A ∪ B) – C = {a, b, c, d, p, q, r} – {a, b, p, q}

= {c, d, r,} (True) 

(v) (A ∪ B) ∩ C = C 

From A ∪ B = {a, b, c, d, p, q, r} 

(A ∪ B) ∩ C = {a, b, c, d, p, q, r} ∩ {a, b, p, q} 

= {a, b, p, q} = C (True)