A set consisting 40 students. 20 of them take maths, 20 take physics and 20 take biology. Present it on a venn?

a: math b: phys c: bio Solution: a = 6; ab = 3; abc = 9; ac = 2; b = 4; bc = 4; c = 5; x = 7; EVERYONE: x+a+b+c+ab+ac+bc+abc= 40 NONE: x= 7 a: a+ab+ac+abc= 20 b: b+ab+bc+abc= 20 c: c+ac+bc+abc= 20 a or b: a+b+ab+ac+bc+abc= 28 a or c: a+c+ab+ac+bc+abc= 29 b or c: b+c+ab+ac+bc+abc= 27 a and b: ab+abc= 12 a and c: ac+abc= 11 b and c: bc+abc= 13 ONLY ONE: a+b+c= 15 ONLY TWO: ab+ac+bc= 9 AT LEAST 2: ab+ac+bc+abc= 18 ALL 3: abc= 9

students taking all subjects = 9 those taking P & B = 13 M & P = 12 M & B = 11 so, let us find the number of students who took only M or B or P for students with M =6 B = 5 P = 4 only one = 6+5+4 = 15 all three = 9 at least two = 8+6+4 = 18 only two = 4+3+2 = 9 =======================================… now, i can't make a venn diagram here but above calculations give you values for every possible combination possible with venn diagram

students taking all subjects = 9 those taking P & B = 13 M & P = 12 M & B = 11 so, let us find the number of students who took only M or B or P for students with M =6 B = 5 P = 4 only one = 6+5+4 = 15 all three = 9 at least two = 8+6+4 = 18 only two = 4+3+2 = 9 =======================================... now, i can't make a venn diagram here but above calculations give you values for every possible combination possible with venn diagram