1 .
Let $n \geq 2$ be an even integer and let $S = \{1,2,3,\dots,n\}$. Consider subsets of $S$ that
contain at least one even number. How many such subsets are there?
(a)
$(n/2) \cdot 2^{n/2}$
(b)
$2^{n} + 2^{n/2}$
(c)
$2^{n/2} + 2^{n/2}$
(d)
$2^{n} - 2^{n/2}$