Question

Are the two expressions ((A.B) + (A.C) + (B.C)).(A.B.C)' ; and

(A.B.C') + (A.C.B') + (B.C.A') equal.

Answer 1

Yes, the two expressions are equal. To show this, we expand both expressions and compare them.

Step-by-step explanation:

Yes, the two expressions ((A.B) + (A.C) + (B.C)).(A.B.C)' and (A.B.C') + (A.C.B') + (B.C.A') are equal.

To show this, let's expand both expressions:

First expression: ((A.B) + (A.C) + (B.C)).(A.B.C)' = (A.B.A.B.C') + (A.B.A.C.C') + (A.B.B.C') + (A.C.A.B.C') + (A.C.A.C.C') + (A.C.B.C') + (B.C.A.B.C') + (B.C.A.C.C') + (B.C.B.C') = A^2B^2C' + A^2BC' + AB^2C' + A^2BC' + AC^2C' + ACC' + ABC^2C' + ACC' + B^2C^2C'

Second expression: (A.B.C') + (A.C.B') + (B.C.A') = ABCC' + ACB'C' + BCA'C'

By comparing the expanded forms of both expressions, we can see that they are equal.