Mathematical Sets on the PSAT/NMSQT
Do you collect stamps, bottle caps, or tissues sneezed in by famous people? If so, your collection is a set. The PSAT/NMSQT doesn’t care about the stuff you display on your wall (though a mental health professional may want to know more about your interest in tissues). The exam evaluates how well you deal with mathematical sets. No worries — all you need to remember are a few facts:

The elements of a set are enclosed by brackets:{–2, –1, 0, 1, 4, 6, 7}

If the set continues, you see three dots after the last element: {2, 4, 6, 8 . . .}

A set with nothing in it — not even one element — is called an empty set and may be represented by brackets with nothing between them: { }. An empty set is usually represented by a crossedout zero:

To find the union of two sets, put them together and then cross out any elements that show up more than once. For example, the union of {5, 5.5, 6, 6.5} and {6, 7, 8} is {5, 5.5, 6, 6.5, 7, 8}.

To find the intersection of two sets, see which elements they have in common. In the preceding bullet, the intersection of the two sets is {6}, because that’s the only common element. If two sets have no common elements, the intersection is an empty set.
If all the PSAT/NMSQT asked you to do was to look at lists of numbers, set questions would be nobrainers. However, they favor questions like “what is the intersection of the set of twodigit prime numbers less than 19 and the set of odd numbers from 11 to 35?” The answer, by the way, is {11, 13, 17}.
Try these two set questions:

How many elements are the intersection of the sets {E, G, I, R} and {I, K, R, S, T}?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 7

Set A = {1, 2, 3, 4, 5}, set B = {2, 4, 6, 8}, and set C = {2, 3, 5, 7}. Which element is not in the union of sets A and C?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Now check your answers:

B. 2
The intersection of two sets is the elements in common. Both sets have the letters I and R, so these two sets have 2 elements in the intersection, Choice (B).

E. 6
The easiest way to do this problem is to simply figure out what the union of sets A and C is, and then look for the answer choice that doesn’t fit. A is {1, 2, 3, 4, 5}, and set C adds only the number 7 into the mix (recall that the union of two sets is the inclusive one — the operation that includes all the numbers in either set).
So, the union of A and C is {1, 2, 3, 4, 5, 7}. Among the answer choices, Choice (E) is the only one that doesn’t belong.