Sets Test - 18...

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.

How many rural uneducated people are employed?

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 $$:$$ $$(7, 15, 31)$$

If $$A=\left\{ 2,4\left\{ 5,6 \right\} ,8 \right\} $$, then which one of the following statements is not correct?

For two sets $$A$$ and $$B$$, $$ A\cap \left( A\cup B \right)=$$

If $$A=\left\{a,b,c\right\},B=\left\{c,d,e\right\},C\left\{a,d,f\right\},$$ then $$A\times \left( B\cup C \right)$$ is

$$A$$ and $$B$$ are two sets having $$3$$ and $$5$$ elements respectively and having $$2$$ elements in common. Then the number of elements in $$A\times B$$ is