Question

Question 1: In a class of 240 students numbered 1 to 240, all even numbered students opt for Chemistry, whose numbers are divisible by 5 opt for Mathematics and those whose numbers are divisible by 7 opt for Physics. How many opt for none of the three subjects?

Answer 1

Let C denote the set of students who had taken Chemistry, M the set of students who had taken Mathematics and P the set of students we had taken Physics. Here m(U)= 240. M(C) = 240 = 120, 4(M)= 240 = 48, 4(P)=[240]={34.28]=34 Students who had opt for both Chemistry and Mathematics are those with numbers divisible by both 2 and 5 te, 10. nienM)2 240 = 24._ Similarly students who had oft for both Mathematics and physics are those with numbers divisible by 5 and tie, 35. ne dine) = [ 34 ] = [6085] = 6 Similarly students who had opt for both Physica and Chemistry are those with numbers divisible by tand 2 il, 14 mcp nC) = 124 ]= (17.14] = 17._ Also students who had opted for all three subjects are mpenmnP)=24]=[3.42] = 3 2. Number of students who opt for home of the subjects = n(u) - uluMUP) EM(U) - [M(C) tu[M]+u(P)-u(enml-m(MOP)-u( Pnc)+ ulenmne)] Z 240 - [120 +48 +34-24-6-17 +3] Z240 - 158 = 82. (Answer)