Question

1.
An examination was conducted in physics, chemistry and mathematics. It P, C, M denote
respectively the sets of students who passed in Physics, in Chemistry and in
Mathematics, express the following sets using union, intersection and difference symbols.
(a) Set of candidates who passed in mathematics and chemistry, but not in physics;
(b) Set of candidates who passed in all the three subjects;
(c) Set of candidates who passed in mathematics only;
(d) Set of candidates who failed in mathematics, but passed in at least one subject.
(e) Set of candidates who passed in at least two subjects;
(f) Set of candidates who failed in one subject only.​

Answer 1

HERE IS YOUR ANSWER

Set of candidates who failed in mathematics,but passed in at least two subjects

    = M' intersection ( P union C )  

here M' is complement of M , that is who failed in Maths (M) and also solved in P or C or both

Set of candidates who failed in one subject only.

       = (P' intersection M intersection C ) union ( P intersection M' intersection C) union( P intersection M intersection C')

 

Here in first part student failed in physics but passed in maths and chemistry , in second part failed in maths but passed in other two and in third failed in chemistry and passed in others.

usually or  is denoted by union combing these parts and giving the required solutuon.