Question

For any sets A ,B and C ,Prove that A – (B U C) = (A-B) n (A – C)​

Answer 1

Answer:

Let A, B, and C be three sets. Prove that A-(BUC) = (A-B) ∩ (A-C)

Solution)

L.H.S = A - (B U C)

A ∩ (B U C)c

A ∩ (B c ∩ Cc)

(A ∩ Bc) ∩ (A∩ Cc)

(AUB) ∩ (AUC)

R.H.S = (A-B) ∩ (A-C)

(A∩Bc) ∩ (A∩Cc)

(AUB) ∩ (AUC)

L.H.S = R.H.S

Answer 2

$\large {\mathtt {\red{\underbrace {\overbrace{\blue{\boxed {\boxed{\pink{- QUESTION\\ -}}}}}}}}}$

For any sets A ,B and C ,Prove that A – (B U C) = (A-B) n (A – C)​

$\large {\mathtt {\red{\underbrace {\overbrace{\blue{\boxed {\boxed{\pink{- ANSWER\\\\ -}}}}}}}}}$

L.H.S = A - (BUC)

        = A ∩ (B U C)'

       = A ∩ (B' ∩ C')

       = (A ∩ B') ∩ (A∩ C')

       = (AUB) ∩ (AUC)

R.H.S = (A - B) ∩ (A - C)

         = (A ∩ B') ∩ (A ∩ C')  

         = (A U B) ∩ (A U C)

HENCE LHS=RHS

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