Question

Column A	Column B
(a) If E1 and E2 are the two mutually exclusive events	(i) E1 ∩ E2 = E1
(b) If E1 and E2 are the mutually exclusive and exhaustive events	(ii) (E1 – E2) ∪ (E1 ∩ E2) = E1
(c) If E1 and E2 have common outcomes, then	(iii) E1 ∩ E2 = Φ, E1 ∪ E2 = S
(d) If E1 and E2 are two events such that E1 ⊂ E2	(iv) E1 ∩ E2 = Φ

Answer 1

Column A	Column B
(a) If E1 and E2 are the two mutually exclusive events	(iv) E1 ∩ E2 = Φ
(b) If E1 and E2 are the mutually exclusive and exhaustive events	(iii) E1 ∩ E2 = Φ, E1 ∪ E2 = S
(c) If E1 and E2 have common outcomes, then	(ii) (E1 – E2) ∪ (E1 ∩ E2) = E1
(d) If E1 and E2 are two events such that E1 ⊂ E2	(i) E1 ∩ E2 = E1

Explanation:

(a) If E₁ and E₂ are mutually exclusive events, then E₁ ∩ E₂ = Φ.

(b) If E₁ and E₂ are mutually exclusive and exhaustive events then E₁ ∩ E₂ = Φ and E₁ ∪ E₂ = S.

(c) If E₁ and E₂ have common outcomes, then (E₁ – E₂) ∪ (E₁ ∩ E₂) = E₁

(d) If E₁ and E₂ are two events such that

E₁ ⊂ E₂ ⇒ E₁ ∩ E₂ = E₁