In a sophomore class of 80 students, 42 students take Spanish, 24 take French and 4 students take both Spanish and French How many students in this class are not enrolled in either Spanish or French?

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Solution

The correct option is A 18
Let $S, F$ be the sets representing number of students who take Spanish and French respectively.
According to question,
$| S | = 42, | F | = 24, | S \cap F | = 4$
$∴ | S \cup F | = | F | + | S | - | F \cap S | = 42 + 24 - 4 = 62$
Number of students not enrolled in either Spanish or French $= | U | - | S \cup F | = 80 - 62 = 18$
Hence, option A is correct.

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