Question

Under which of the following conditions will evaluating this boolean expression

Answer 1

1.) 
((i <= n) && (a[i] == 0)) || (((i >= n) && (a[i-1] == 0))) 

The expression will be true IF the first part is true, or if the first part is false and the second part is true. This is because || uses "short circuit" evaluation. If the first term is true, then the second term is *never even evaluated*. 

For || the expression is true if *either* part is true, and for && the expression is true only if *both* parts are true. 

a.) (i <= n) || (i >= n) 

This means that either, or both, of these terms is true. This isn't sufficient to make the original term true. 

b.) (a[i] == 0) && (a[i-1] == 0) 

This means that both of these terms are true. We substitute. 

((i <= n) && true) || (((i >= n) && true)) 

Remember that && is true only if both parts are true. So if you have x && true, then the truth depends entirely on x. Thus x && true is the same as just x. The above predicate reduces to: 

(i <= n) || (i >= n) 

This is clearly always true.