A year group contains $50$ students. $$n(A)=31,\qquad n(B)=27.$$ Find the least and greatest possi

Question

A year group contains $50$ students. $$n(A)=31,\qquad n(B)=27.$$ Find the least and greatest possible values of $n(A\cap B)$. Find the least and greatest possible numbers belonging to exactly one set. Can exactly $15$ students belong to exactly one set? Justify your answer.

Accepted Answer

(a) $8$ to $27$ (b) $4$ to $42$ (c) No; the exactly-one count must be even

Sets

Sets