The answer is A. The rest of the answers are not necessarily correct with the operations.
Answer:
To prove:
X+Y.Z=(X+Y).(X+Z)
Taking R.H.S
= (X+Y).(X+Z)
By distributive law
= X.X+X.Z+X.Y+Y.Z --- (1)
From Boolean algebra
X.X = X
X.Y+X.Z = X.(Y+Z)
Using these in (1)
=X+X(Y+Z)+Y.Z
=X(1+(Y+Z)+Y.Z --- (2)
As we know (1+X) = 1
Then (2) becomes
=X.1+Y.Z
=X+Y.Z
Which is equal to R.H.S
Hence proved,
X+Y.Z=(X+Y).(X+Z)
