Q1Discrete Mathematics Structure

Question

Participation in sports is compulsory in a college. In a class of 80 students, 60 play football, 40 play basketball. Find : (i) how many play both the games (ii) how many play football only

Answer 1

Let $F$ be the set of football players and $B$ be the set of basketball players. $∣ F \cup B ∣ = 80$ , $∣ F ∣ = 60$ , $∣ B ∣ = 40$ .

(i) Both games: $∣ F \cap B ∣ = ∣ F ∣ + ∣ B ∣ - ∣ F \cup B ∣ = 60 + 40 - 80 = 20$ .
(ii) Football only: $∣ F - B ∣ = ∣ F ∣ - ∣ F \cap B ∣ = 60 - 20 = 40$ .

Q1Discrete Mathematics Structure

Question

Answer