Set Theory Test...

S = {1, 2, 3, 5, 8, 13, 21, 34 }. Find $$\displaystyle \sum $$ max (A), where the sum is taken over all 28 elements subsets A to S.

There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

The dual of $$-p\wedge (q\vee \sim r)$$ is

If $$S$$ represents the set of all real numbers $$x$$ such that $$1\le x \le 3$$ and $$T$$ represents the set of all real numbers $$x$$ such that $$2 \le x \le 5$$, the set represented by $$S \cap T$$ is

In a town of $$10,000$$ families it was found that $$40\%$$ families buy newspaper $$A$$, $$20\%$$ families buy newspaper $$B$$ and $$10\%$$ families buy newspaper $$C$$. $$5\%$$ families buy $$A$$ and $$B$$, $$3\%$$ buy $$B$$ and $$C$$ and $$4\%$$ buy $$A$$ and $$C$$. If $$2\%$$ families buy all the three newspaper, find the number of families which buy (i) $$A$$ only (ii) $$B$$ only (iii) none of $$A, B$$ and $$C$$

Suman is given an aptitude test containing 80 problems, each carrying I mark to be tackled in 60 minutes. The problems are of 2 types; the easy ones and the difficult ones. Suman can solve the easy problems in half a minute each and the difficult ones in 2 minutes each. (The two type of problems alternate in the test). Before solving a problem, Suman must spend one-fourth of a minute for reading it. What is the maximum score that Suman can get if he solves all the problems that he attempts?

Which one of the following is correct?

Let $$A = [\theta : sin (\theta) = tan (\theta)]$$ and $$B = [\theta : cos (\theta) = 1]$$ be two sets. Then,

If $$20$$% of three subsets (i.e., subsets containing exactly three elements) of the set $$A = \left \{a_{1}, a_{2}, ...., a_{n}\right \}$$ contain $$a_{2}$$, then the value of $$n$$ is

Let $$A_{1}, A_{2}, ........., A_{m}$$ be m sets such that $$O(A_{i}) = p \forall i = 1, 2, ......... m$$ and $$B_{1}, B_{2}, .........., B_{n}$$ be n sets such that $$O(B_{j}) = q \forall j = 1, 2, ........., n$$. If $$\bigcup_{i=1}^{m} A_{i}$$ = $$\bigcup_{j=1}^{n} B_{j} = S$$ and each element of S belongs to exactly $$\alpha$$ number of $$A_{i}'s$$ and $$\beta$$ number of $$B_{j}'s$$, then