Answer:
11) The intersection of two sets is the set of the elements that are common for both sets, in this case, we can see that: 79, 83 and 99 appear in both sets, then the intersection is: {79, 83, 99}
12) the union of both sets (all the possible options in the selection) is:
{75, 79, 82, 83, 94, 99, 101, 105} and the intersection set is {79, 83, 99}
So we have 8 elements in total, and 3 of them belong to the intersection, then the probability of selecting at random one element that belongs in the intersection is:
p = 3/8 = 0.375
13) In this case, the universal set is the set of all the real numbers.
You can remember that the set of all real numbers is equal to the union of the sets of the rational numbers and the set of the irrational numbers (and those two sets do not share any element).
Then, if we have only the set A = set of the irrational numbers, the complement will be the set of the rational numbers, because we must have that:
Set A U complement = Real set = irrational U rational.
(where U stands for "union")
now we replace Set A = irrational.
Irrational U complement = irrational U rational
complement = rational.
