Q. 524.6( 12 Votes )

Match the followi

Answer :


(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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