Set Theory Test...

In a certain group of 36 people, 18 are wearing hats and 24 are wearing sweaters. If six people are wearing neither a hat nor a sweater, then how many people are wearing both a hat and a sweater ?

While preparing the progress reports of the students, the class teacher found that 70% of the students passed in Hindi, 80% passed in English  and only 65% passed in both the subjects. Find out the percentage of students who failed in both the subjects.

How many students in this group are not taking any of the three subjects?

Let $$\displaystyle A= \left \{ 7,8,9,a,b,c \right \} $$ and $$\displaystyle B= \left \{ 1,2,3,4 \right \} $$ then number of universal relation from the set $$A$$ to set $$B$$ and set $$B$$ to set $$A$$ are

If two intersecting circles with two points in common are drawn then how many common chords can be drawn? Draw the figure and write the answer

The set of natural number is subset of set of real numbers.

$$A=\left\{ x:x\neq x \right\} $$ represents-

Which of the following statements is false?

Let $$A = \{2,3,5,7,8,11\}$$ then which among the following is true?