Answer:
1) If and only if a and b have different values
Explanation:
Given
Expression: !(!a || b) || (!a && b)
Required
When is it true?
The expression is true when the values a and b are different and the proof is as follows.
(1) Assume that: a = true and b = false
!(!a || b) || (!a && b)
= !(!true || false) || (!true && false)
!true = false, so the expression becomes:
= !(false|| false) || (false && false)
In boolean, false|| false = false and false && false = false. So, we have:
= !(false) || (false)
!(false) = true, so, the expression becomes:
= true || (false)
Lastly, true || false = true
(2) Assume that: a = false and b = true
!(!a || b) || (!a && b)
= !(!false|| true) || (!false && true)
!false = true, so the expression becomes:
= !(true|| true) || (true && true)
In boolean, true|| true = true and true && true = true. So, we have:
= !(true) || (true)
!(true) = false, so, the expression becomes:
= false|| true
Lastly, false || true = true
<em>This expression is false if a and b have the same value</em>
