The statement (A + B) – (C’ ⋂ B) = (A + C) is an identity. (Hint: draw a Venn diagram of the LHS and RHS).a.Trueb.False
Question
The statement (A + B) – (C’ ⋂ B) = (A + C) is an identity. (Hint: draw a Venn diagram of the LHS and RHS).a.Trueb.False
Solution
The statement is False.
To understand why, let's break it down using a Venn diagram and the laws of Boolean algebra.
The left-hand side (LHS) of the equation is (A + B) – (C' ⋂ B). This means the union of A and B, minus the intersection of the complement of C and B.
The right-hand side (RHS) of the equation is (A + C). This means the union of A and C.
If we draw a Venn diagram, it's clear that these two sides are not equal. The LHS includes all of A
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