CODEWITHSUNDEEP
booleanboolean-logicboolean-expression
DonnellyOverflow
DonnellyOverflow

Reputation: 4195

Boolean Expression Confusion

A = S•T + V•W + R•S•T

(where • is AND and + is OR)

The answer given says that commutative and distributive laws have been used. However, I can’t get to the answer.

I use commutative and distributive to make

    A = S•T + R•S•T + V•W
    A = S•T + S•T•R + V•W
    A = (S•T + S•T)•R + V•W
    A = S•T•R + V•W

whereas the answer says:

    A = S•T + V•W

and Wolfram Alpha confirms the answer. I'm just wondering how it's done.

Upvotes: 2

Views: 102

Answers (2)

Paul R
Paul R

Reputation: 212949

It's simply that the R*S*T term is redundant, since you already have S*T in the expression, so the state of R is irrelevant.

More formally:

A = S•T + R•S•T + V•W

Collect terms:

A = (1+R)•S•T + V•W

1+R = 1, so drop this to get:

A = S•T + V•W

Upvotes: 2

Robert Levy
Robert Levy

Reputation: 29073

Let's just look at this bit:

S•T + R•S•T

The right side of the OR can be completely ignored because it defines a subset of the left side of the OR. If S•T is true, then S•T+anything will be true

Upvotes: 1

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