Verified answer

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Prove that A - (BUC) = (A-B) ∩ (A-C)

This is a discussion on Prove that A - (BUC) = (A-B) ∩ (A-C) within the Discrete Mathematics, Set Theory, and Logic forums, part of the University Math category; Let A, B, and C be three sets. Prove that A-(BUC) = (A-B) ∩ (A-C) Solution) L.H.S = A - ...

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

Is this correct?

(A ∩ Bc) ∩ (A∩ Cc) = (AUB) ∩ (AUC) , this is not correct you could use

A ∩ Bc = A - B , and A∩ Cc=A - C

In fact

(A ∩ Bc) = (AcUB)c

The red lines are false are and they are not useful, you solved it but the last lines are not equal to the previous ones

see web page for "red" lines