Types of Sets

In a class of 50 students 35 opted for Maths, 37 opted for commerce. The number of such students who opted for both maths and commerce is _____.

Two finite sets respectively have $x$ and $y$ number of elements. The total number of sub sets of the first is $56$ more than the total no. of sub sets of the second. The value of $x, y$ are respectively __________

The set of cubes of natural numbers is

The set of integers between $-5 \mathrm{and} 5$.

The set $A=\left\{x:x\in R, x^2=16 \& 2x=6\right\}$ equals

Set $\mathrm{A}$ has $5$ elements, set $\mathrm{B}$ has $4$ elements. How many relations are possible between $\mathrm{A}$ and $\mathrm{B}$?

Let $\mathrm{U}$ be the Universal Set, $\mathrm{A}$ be any finite set then $\left(\mathrm{A}\cap \mathrm{U}\right)=$

As per question No.$\left(21\right)$ with same order of options (a) (b) (c) and (d) list the losing conditions.

As per question No.$\left(21\right)$ with same order of options (a) (b) (c) and (d) list the blocking conditions.

If four members $a,b,c,d$ of a decision making body are in a meeting to pass a resolution where rule of majority prevails list the wining coalitions. Given that $a,b,c,d$ own $50\%$, $20\%,15\%,15\%$ shares each.

If $A=\{0,1\}$ state which of the following statements are true:- (i) $\left\{1\right\}\subset \mathrm{A}$ (ii) $\left\{1\right\}\in \mathrm{A}$ (iii) $\varphi \in A$ (iv) $0\in A$ (v) $1\subset A$ (vi) $\left\{0\right\}\in A$ (vii) $\varphi \subset A$

with the same order of options (a), (b), (c) and (d) find the number having only coffee.

If $f\left(x\right)=1/1-x$, then $f^{-1}\left(x\right)$ is

$\left\{\right(x,y)\mid x<y\}$ where $x,y\in R$ is

$\left\{(x,y),y=x^2\right\}$ where $x,y\in R$ is

$\left\{\right(x,y)\mid x=4\}$ where $x,y\in R$ is a

$\left\{\right(x,y)\mid x+y=5\}$ where $x,y\in R$ is a

If $E=\{1,2,3,4,5,6,7,8,9\}$, the subset of $E$ satisfying $5+x>10$ is

$A\cup A\text{'}$ is equal to $(E$ is a superset of $A)$

$A\cap \varphi$ is equal to $(E$ is a superset of