Answer to Question #311562 in Algorithms for OSEGO

Question

The formula (A∨B) ∧ (¬B ∨C) simplifies down to which of the following when using Boolean algebra?

A. A ∧ C

B. A ∧ B ∨ C

C. A ∨ C

D. B

E. A ∧ ¬B ∨ C

Answer 1

Prove that none of the variants is correct:

$A:\\A=1,B=0,C=0:\left( A\lor B \right) \land \left( \lnot B\lor C \right) =1,A\land C=0\\B:\\A=1,B=1,C=0:\left( A\lor B \right) \land \left( \lnot B\lor C \right) =0,A\land B\lor C=1\\C:\\A=0,B=0,C=1:\left( A\lor B \right) \land \left( \lnot B\lor C \right) =0,A\lor C=1\\D:\\A=1,B=0,C=0:\left( A\lor B \right) \land \left( \lnot B\lor C \right) =1,B=0\\E:\\A=0,B=0,C=1:\left( A\lor B \right) \land \left( \lnot B\lor C \right) =0,A\land \lnot B\lor C=1$