The shaded region in the venn diagram above is

In a class of 40 students,each student offers at least one of physics and chemistry. If the number of students that offers physics is 3 times the number that offer both subject and the number that offer chemistry is twice the number that offer physics. Find the number of students that offers physics only

Given U ={Even number between 0 and 32 }

         P = {Multiples of 6 between 0 and 30}

         Q ={Multiples of 4 between 0 and 30}

Find ${{(P\cup Q)}^{c}}$

In a  class of 40 students, 32 offers Mathematics, 24 offers physics and 4 offers neither Mathematics nor physics. How  many offer both Mathematics and Physics?

In a school, 220 students offer Biology or Mathematics or both 125 offer Biology and 110 Mathematics. How many offer Biology but not Mathematics?

In a youth club with 94 members, 60 like modern music and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?

Let P ={1, 2, u, v, w, x}

           Q = {2,3, v,w, 5, 6, y}

and R = {2,3, 4, v, x, y}. Determine (P – Q)∩R