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Prove algebracally (x+y).(x+z)=x+yz

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L.H.S. = (X + Y)(X + Z) = XX + XZ + XY + YZ

= X + XZ + XY + YZ (XX = X Indempotence law)

= X + XY + XZ + YZ = X(1 + Y) + Z(X + Y)

= X.1 + Z(X + Y) (1 + Y = 1 property of 0 and 1)

= X + XZ + YZ (X . 1 = X property of 0 and 1)

= X(1 + Z) + YZ

= X.1 + YZ (1 + Z = 1 property of 0 and 1)

= X.1 + YZ (X . 1 = X property of 0 and 1)

= L.H.S. Hence proved.

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