Why is `!!(a||!a)` always true?

I’m a Java rookie and in School we got some homework. I shall explain boolean terms but I don’t understand one of them.

The question is

Why is this expression always true?

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!!(a||!a)

I understand the part in the brackets but what do the two exclamation marks in front of it?

If the first a = true –> !a = not true –> !! ( double negation = true?) a = true and the second !a = not true –> !!a = true –> !!!a = not true

and if I’m right , why is this expression alsways true? That beats me.

Could any of you explain that to me?

Thanks for your help!

>Solution :

First off, !! expression cancels out: it’s the same as expression, because the negation of a negation is the original value.

So we’re left with a || ! a, which is a disjunction. So the result is true if at least one of the sub-expressions a or !a is true.

And lastly, a is true if a is true (duh). And ! a is true if a is false. Thus, regardless of the value of a, the overall expression is true.