Question

Please show steps with explanations: I) Circle each expression which is true. Some are Boolean axioms and theorems. (Hint: if you are not sure, use truth table to help you determine.) a· x-x=1 d. x ty z-(x +y) - (x + z)

Answer 1

x . bar x = 1 Truth Table: x . bar x always zero not 1 Hence expression (a) is wrong x + 1 = 1 Truth Table x + 1 always equal to 1 Hence expression (b) is True x + bar x . y \r\n By observing Truth table x + bar x y notequalto y Hence expression (c) is wrong (x + y z) = (x + y) . (x + z) L . H . S = x + y z R . H . S = (x + y) . (x + z) = x (x + z) + y (x + z) R . H . S = x . x + x z + y x + y z Rightarrow R . H . S = x + x z + y x + y z [Because A . A = A] R . H . S = x (1 + z + y) + y z R . H . s = x (1) + y z [Because 1 + A = 1] r . H . S = x + y z = L . H . S Here A = z + y L . H . S = R . H . S Hence expression (d) is True \r\n x . bar x = 1 x + 1 = 1 True x +