First slide

Operations on Sets

Question

$A, B, C$ are the sets of letters needed to spell
the words STUDENT, PROGRESS and CONGRUENT,
respectively. Then $n (A \cup (B \cap C))$ is equal to

Moderate

A

8
B

9
C

10
D

11

Solution

$\begin{array}{l} A = {D, E, N, S, T, U] \\ B = {E, G, O, P, R, S} \\ C = {C, E, G, N, O, R, T, U} \end{array}$
So $\begin{array}{l} A \cup (B \cap C) \\ = {D, E, N, S, T, U} \cup {E, G, O, R} \\ = {D, E, G, O, N, R, S, T, U} \end{array}$
and $n [(A \cup (B \cap C)] = 9$

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