CODEWITHSUNDEEP
boolean-logicboolean-expression
Olivia
Olivia

Reputation: 51

Why does this boolean expression reduce to 1?

The expression is: x' + x + xz + yz - which reads x not or x or x and z or y and z. This expression is the reduced form of a very large expression which I am trying to prove equal to 1.

I know the above expression is equivalent to 1 according to Wolfram and another expression reducer. Any explanation would be very helpful. Thank you in advance.

Upvotes: 0

Views: 220

Answers (2)

maks
maks

Reputation: 6006

The key to understanding this expression is idea of or operator. If you have true or false or smth there is no matter what is smth, the expression still will be true. So in your case xz + yz is redundant here because x' + x covers all the set of possible values

Upvotes: 2

Ted Hopp
Ted Hopp

Reputation: 234795

We'll assume that Wolfram uses 1 as a synonym for true. The first two terms of the expression are x' and x. One or the other of them must be 1 (true), so the logical OR of the two of them is 1. Then the logical OR of true and anything else is going to be true. That's why the entire expression reduces to 1.

Upvotes: 4

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