The expression C + C′ pairs a Boolean variable with its own complement (its logical NOT) using the OR operation. The result is governed by the complement law of Boolean algebra, sometimes called the law of the excluded middle: a statement is either true or its negation is true, so their OR is always true.

Because a Boolean variable can take only two values, we can verify the law by full enumeration:

In both rows exactly one of C and C′ is 1, and OR outputs 1 whenever at least one input is 1. Therefore C + C′ = 1 for every value of C, which is the correct answer.

The other choices come from confusing this law with its dual or with the idempotent law. Getting back C would be true for C + C (OR of a variable with itself), not with its complement. The product C · C′ is the dual complement law and equals 0, not 1 — that expression describes when a signal and its inverse are both 1, which never happens. A result of 0 would correspond to C · C′, the AND of a variable with its complement, again the opposite operation from the OR asked here.