Using PMF and CDF to calculate probability Given the following CDF

what is
$$P(T > 3)$$
and according to my answer key it's 1-1/2 = 1/2.
Can someone explain to me why it is 1-F(3), and would subtracting F(3) be subtracting 4 as well? Normally I saw stuff like t = 1,2,3,4,5,6...., but I've never seen something where it skips numbers and stuff like 1,3,5,7, ect ect. How does this affect the cdf and such? In short, I'm mainly confused as to how they figured out it was 1 - F(3).

Recall that by definition, the cumulative distribution function is the probability of having a value less than or equal to the argument of the function. So 
$$
P(T>3) = 1-P(T \leq 3)= 1-F(3) = \frac{1}{2}
$$
What may be confusing you is that you have a piecewise "step" function. That is, there are probability jumps at $1$, $3$, $5$, and $7$, and no increase in the cumulative distribution (or probability for those values) between those integers. 
