Union

Q. If $A=\{x:-1<x<1;x\in R\}$, $B=\{x:x\le 0\text{or}x\ge 2;x\in R\}$ and $A\cup B=R-C$, then set $C$ is

1. $\{x:1<x<2;x\in R\}$
2. $\{x:1<x\le 2;x\in R\}$
3. $\{x:1\le x<2;x\in R\}$
4. None of these

Q. If $A$ is the set of the divisors of $15,B$ is the set of prime numbers less than $10$ and $C$ is the set of even natural numbers smaller than $9,$ then $(A\cup C)\cap B$ is the set

1. $\{1,3,5\}$
2. $\{1,2,3\}$
3. $\{2,3,5\}$
4. $\{2,5\}$

Q. The set A and set B are defined as
$A=\{x:xisanaturalnumber\}$
B = \{-x: x is a whole number\}\)
The union of set A and set B is a set of all .

1. Integers
2. Rational Numbers
3. Real Numbers
4. Integers except 0.

Q.

Suppose $A_1,A_2,.....................,A_{30}$ are thirty sets each having 5 elements each and $B_1,B_2,................B_n$ are $n$ sets each with 3 elements each. Let $\bigcup _{i=1}^{30}{A}_i=\bigcup _{j=1}^n{B}_j=S$ and each element of $S$ belongs to exactly 10 of $A_i$'s and exactly 9 of the $B_j$'s. Then $n$ is equal to

1. $15$

2. $3$

3. $45$

4. $50$

Q. For any two sets $A$ and $B$,
$n\left(AUB\right)\ge n\left(A\right)+n\left(B\right)$
where, $n\left(P\right)$ represents the number of elements in set $P$.

1. False
2. True

Q. On the set of all natural numbers $N,$ set $F_n$ and set $M_n$ gives all factors and all multiples of $n$ respectively for all $n\in N.$ Which of the following statements is/are true?
$1.F_{132}\cap F_{96}=F_{12}2.M_{12}\cup M_{18}=M_{36}3.M_6\cap M_9=M_{18}4.F_{72}\cap F_{60}=F_{12}$

1. $1,2$ and $3$ only
2. $1$ and $3$ only
3. $1,3$ and $4$ only
4. All statements are true

Q. If $A=\{1,2,3\},B=\{4,5,6\},$ then $A\cup B=$

1. $\{1,2,3,4,5,6\}$
2. $\{1,2,3\}$
3. $\{4,5,6\}$

Q.

$\text{For two sets}A=\{5,6,7,8\}\&B=\{7,8,9,11\}.A\cup B=$

1. {5, 6, 7, 8, 9, 10, 11}

2. {5, 6, 7, 8, 9, 11}

3. {9, 11}

4. {5, 6, 7, 8}

Q. Match the following sets with their equal sets.

1. $\{1,2,3,5,6\}$
2. $\{a,b,b,c,c,c\}$
3. $\{6,6,7,3,4,5\}$
4. $\{e,c,d,b,c,a\}$

Q. The smallest set $A$ such that $A\cup \{1,2\}=\{1,2,3,5,9\}$ is

1. $\{2,3,5\}$
2. $\{3,5,9\}$
3. $\{1,2,5,9\}$
4. $\{1,2,\}$

Q. The smallest set $A$ such that $A\cup \{1,2\}=\{1,2,3,5,9\}$ is

1. $\{2,3,5\}$
2. $\{3,5,9\}$
3. $\{1,2,5,9\}$
4. $\{1,2,\}$