Set Theory Test...

Three sets $$A, B, C$$ are such that $$\displaystyle A=B\cap C$$ and $$\displaystyle B=C\cap A$$, then

If n is a member of both set A$$=\left\{\displaystyle\frac{4}{7}, 1, \frac{5}{2}, 4, \frac{1}{2}, 7\right\}$$ and set B$$=\left\{\displaystyle\frac{4}{7}, \frac{7}{4}, 4, 7\right\}$$, which of the following must be true?
I. n is an integer.
II. $$4n$$ is an integer.
III. $$n=4$$

If the universal set $$\{x\in W ,3<x≤12\} ,A=\{5,7,9\}$$, then $$A'=$$

$$(P\cap Q)' \cup R$$

For any two sets $$A$$ and $$B$$, $$A-\left( A-B \right) $$ equals

In a class, $$20$$ opted for Physics, $$17$$ for Maths, $$5$$ for both and $$10$$ for other subjects. The class contains how many students?

In a class of 250 students, 175 take mathematics and 142 take science. How many take both mathematics

and science? (All take math and/or science.)

If X is a finite set. Let $$P(X)$$ denote the set of all subsets of X and let $$n(X)$$ denote the number of elements in X. If for two finite subsets $$A, B, n(P(A)) = n(P(B)) + 15$$ then $$n(B) = $$ ____, $$n(A) =$$ _____

P, Q and R are three sets and $$\xi = P\cup Q\cup R$$. Given that $$n(\xi) = 60, n (P\cap Q) = 5, n(Q\cap R) = 10, n(P) = 20$$ and $$n(Q) = 23$$, find $$n(P\cup R)$$