# 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

and may be represented by brackets with nothing between them: { }. An empty set is usually represented by a crossed-out zero:*empty set*To find the

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}.*union*To find the

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.*intersection*

If all the PSAT/NMSQT asked you to do was to look at lists of numbers, set questions would be no-brainers. However, they favor questions like “what is the intersection of the set of two-digit 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.