Simplify if condition boolean expression

Question

I have this if-condition in my code:

if (a||a&&!b){
// do some stuff
}

with that intial values from my junit test:

boolean a=true, b = true;

as I recognized later the statement can be simplified to:

if (a&&b)

becomes green: Assert.assertTrue(a||a&&!b == a&&b);

Are there any further simplifications? How could I have recognized that this boolean expression could be simplified?

Answer 1

a || a && !b 

is not equal to

a && b

It is equal to just a.

I suppose that in your JUnit test you used a specific combination of values for a and b where the results match, but that does not mean that the expressions are equivalent—and in fact they aren't. A quick way to convince yourself of that is checking the combination

a = true, b = false;

Your original expression clearly yields true for all cases where a == true, but your second expression will yield false whenever b == false.

As for a formal proof of equivalence to just a, take the expansion

a == a && (b || !b)
  == a && b || a && !b

Plugging into your original expression:

a || a && !b == a && b || a && !b || a && !b
             == a && b || a && !b
             == a