boolean logic - Why does (not false and true or not false and not true) come out to True?

Question

Why does (not false and true or not false and not true) come out to True?

If we evaluate in order, from left to right, we will have an and statement at the end with a not true. Shouldn't this come out to false?

question from:https://stackoverflow.com/questions/65922900/why-does-not-false-and-true-or-not-false-and-not-true-come-out-to-true

Answer 1

Because operator precedence.

Check the documentation for the operators in the language you're using to see their specific rules. But at least in every language I've used the and operation takes precedence over the or operation.

So this:

not false and true or not false and not true

Is the same as this:

(not false and true) or (not false and not true)

The not operation has even higher precedence, so now it's the same as this:

((not false) and true) or ((not false) and (not true))

Which reduces to:

(true and true) or (true and false)

Which reduces to:

true or false

Which reduces to:

true