Subset

Q. If two sets $A$ and $B$ have $99$ elements in common, then the number of elements common to each of set $A\times B$ and $B\times A$ are

1. $2^{99}$
2. ${99}^2$
3. $100$
4. $18$

Q. The relation $R$ on $R$ defined as $R=\left\{\right(a,b):a\le b\},$ is

1. reflexive relation
2. transitive relation
3. symmetric relation
4. equivalence relation

Q.

State which of the following are null or empty sets?

$\left\{CapitalsofthesatesofIndia\right\}$

Q. If P, Q and R are subsets of a set A, then $R\times (P^c\cup Q^c{)}^c=$

1. $(R\times P)\cap (R\times Q)$
2. $(R\times Q)\cap (R\times P)$
3. $(R\times P)\cup (R\times Q)$
4. $Noneofthese$

Q. The Boolean expression $\sim (p\vee q)\vee (\sim p\wedge q)$ is equivalent to

1. $\sim p$
2. $\sim q$
3. $p$
4. $q$

Q. Which set is the subset of all given sets

1. $\{1,2,3,\mathrm{4...}\}$
2. $\left\{1\right\}$
3. $\left\{0\right\}$
4. $\left\{\right\}$

Q. Let $A\&B$ be two sets containing four and two elements respectively such that $A\cap B=\varphi$. Then the number of subsets of set $A\times B$ each having at least five elements is

Q. Let $P,Q,R,S$ be the four sets such that $P=\{3,5,7,9,11\},Q=\{9,11,13\},$ $R=\{3,5,9\}$ and $S=\{13,11\}$. Which of the following options is/are correct?

1. $R\subset P$
2. $Q\subset P$
3. $R\subset S$
4. $S\subset Q$

Q.

If $A=\varnothing$ , the number of subset is __________ and the number of proper subsets is __________.

Q. Let $S$ be a non-empty subset of $R$. Consider the following statement
$p:$ there is a rational number $x\in S$ such that $x>0$. The negation of $p$ is

1. There is a rational number $x\in S$ such that $x\le 0$
   
2. There is no rational number $x\in S$ such that $x\le 0$
   
3. Every rational number $x\in S$ such that $x\le 0$
   
4. $x\in S$ and $x\le 0\Rightarrow x$ is not rational

Q. If two sets $A\&B$ are equal to one another then $A\subseteq B.$

1. False
2. True

Q. If the solution set of $|x-k|<2$ is a subset of the solution set of the inequality $\frac{2x-1}{x+2}<1,$ then the number of possible integral value(s) of $k$ is

1. $0$
2. $1$
3. $2$
4. $3$

Q.

If $X=\{8^n-7n-1|nϵN\}$ and $Y=\{49n-49|nϵN\}$, then

1. $X\subset Y$

2. $Y\subset X$

3. $X=Y$

4. $X\cap Y=\varphi$

Q. If $A=\{a,c,e\}\text{and}B=\{a,b,c,d,e,f\}$ then the value of $A\Delta B$ is

1. $\{b,d,f\}$
2. $\left\{b\right\}$
3. $\{a,c,e\}$
4. $\{d,f\}$

Q. If $X=8^n-7n-1,n\in NandY=49(n-1),n\in N$, then -

1. $X\subset Y$
2. $Y\subseteq X$
3. $X=Y$
4. None of these

Q. $100$ students of class $12th$ opted for Mathematics while $90$ students opted for Biology. $170$ students opted for Mathematics or Biology. How much students opted for Mathematics and Biology?

1. $360$
2. $190$
3. $20$
4. None of the above