3. Prove algebraically that ( X - Y)(X +Z) = X + YZ
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Explanation:
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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