Q. 524.6( 13 Votes )

# Match the followi (i) ((A′ B′) – A)′

[(A′ B′) – A]′

= [(A′ B′) A’]’

{ A – B = A B’}

= [(A B)’ A’]’

{ (A B)’ = A’ B’}

= [(A B)’]’ (A’)’

= (A B) A

= A

((A′ B′) – A)′ = A

(ii) [B′ (B′ – A)]′

[B′ (B′ – A)]′

= (B’)’ (B’ – A)’

{ (A B)’ = A’ B’}

= B (B’ A’)’

{ A – B = A B’}

= B [(B’)’ (A’)’]

{ (A B)’ = A’ B’}

= B (B A)

= B

[B′ (B′ – A)]′ = B

(iii) (A – B) – (B – C)

Step 1: A – B

Step 2: B – C

Step 3: (A – B) – (B – C)

Clearly, the Venn diagram in Step 3 shows same region as in Step 1

Hence, (A – B) – (B – C) = A – B

(iv) (A – B) (C – B)

Step 1: A – B

Step 2: C – B

Step 3: (A – B) (B – C)

Clearly, from the Venn diagram in Step 3:

(A – B) (B – C) = A C – B

(v) A × (B C)

Let y A × (B C)

y A and y (B C)

y A and (y B and y C)

(y A and y B) and (y A and y C)

y (A × B) and y (A × C)

y (A × B) (A × C)

A × (B C) = (A × B) (A × C)

(vi) A × (B C)

Let y A × (B C)

y A and y (B C)

y A and (y B or y C)

(y A and y B) or (y A and y C)

y (A × B) or y (A × C)

y (A × B) (A × C)

A × (B C) = (A × B) (A × C)

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