Set Theory Test...

How many of these students are taking physics?

A survey was carried out to find out the types of shampoo that a group of $$150$$ women have tried. It was found that $$84$$ women have used brand A shampoo, $$93$$ have used brand B, and $$69$$ have used brand C of these women, $$45$$ have tried brands A and B, $$25$$ have tried brands A and C and $$40$$ have tried brand B and C. Determine the number of women who have tried (a) all three brands, (b) only brand A

Which one of the following is incorrect?

The number of elements of the set $$\left \{ x:x\in Z,x^{2}=1 \right \}$$ is :

If $$A \subset B$$, then $$A \cap B$$ is

Let $$A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$. Then the number of subsets of $$A$$ containing exactly two elements is

In a class of $$60$$ students, $$45$$ students like music, $$50$$ students like dancing, $$5$$ students like neither. Then the number of students in the class who like both music and dancing is

Let $$A_1, A_2$$ and $$A_3$$ be subsets of a set $$X$$. Which one of the following is correct?

Statements:
I. Some Politicians are social workers.
II. All Doctors are social workers.
Conclusions:
I. Some Doctors are Politicians.
II. Some social workers are Doctors as well as Politicians.

From among the given alternatives select the one in which the set of numbers is most like the set of numbers given in the question.
Given set $$:$$ $$(7, 15, 31)$$