Equal, Equivalent and Unequal Sets

Q. If $R=\{x:x^2=7\},S=\{x:x+4=4\}$ and $T=\{x:x^2+2=8\}$, then which of the following is correct?

1. $R$ and $T$ are equal sets.
2. $R$ and $S$ are equal sets.
3. $S$ and $T$ are equal sets.
4. None of them are equal sets.

Q. Choose the correct pair of equal sets.

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

Q. $A$ is set of letters of the word 'SARIKA', $B$ is set of letters of the word 'RAKASI', then $A$ and $B$ are

1. equivalent but not equal
2. equal but not equivalent
3. equal and equivalent
4. neither equal nor equivalent

Q. The most appropriate option for the following sets
$A$ is set of letters of the word 'NARAYANA'
$B$ is the set of letters of the word 'ARANYA'

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are equal sets
3. $A$ and $B$ are disjoint sets
4. $n\left(A\right)>n\left(B\right)$

Q. Two sets are said to be unequal if they have different elements but same cardianalities.

1. True
2. False

Q. $A$ is set of letters of the word 'NARAYANA'
$B$ is the set of letters of the word 'ARANYA'.
Then which of the following option is incorrect ?

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are equal sets
3. $n\left(A\right)=n\left(B\right)$
4. $n\left(A\right)>n\left(B\right)$

Q. $A$ is set of letters of the word 'debit card'
$B$ is the set of letters of the word 'bad credit'.
Then which of the following options is/are correct ?

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are unequal sets
3. $A$ and $B$ are equal sets
4. $n\left(A\right)=n\left(B\right)$

Q. Match the following: $$\begin{array}{cc}\text{Column A}& \text{Column B}\\ 1.\{1,2,4,8\}& A.\{x:x\text{is a natural even number less than 10}}\\ 2.\left\{2\right\}& B.\{x:x\text{is a prime number and a divisor of 8}}\\ 3.\{2,4,6,8\}& C.\{x:x\text{is a divisor of 8}}\\ 4.\{4,6,8,9\}& D.\{x:x\text{is a composite number less than 10}\}\end{array}$$

1. 1 - C, 2 - A, 3 - B, 4 - D

2. 1 - B, 2 - D, 3 - A, 4 - C

3. 1 - A, 2 - D, 3 - C, 4 - B

4. 1 - C, 2 - B, 3 - A, 4 - D

Q. Choose the correct pair of Equivalent Sets.

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

Q.

Which of the following is/are equal sets?

1. A = Set of prime numbers less than 6

   B = set of prime factors of 30

2. A = {x: x - 5 = 0}

   B = {x: x is a positive integral root of the equation $x^2$-2x-15=0 }

3. A = {x: x is even integer and x ≤ 10}

   B = {2, 4, 6, 8, 10}

4. A = {x: x is a letter in the word FELLOW}

   B = {y: y is a letter in the word WOLF}

Q. Two sets $A=\{a,b,c,d\}$ and $B=\{b,c,d,x\}$ are equal sets, iff $x=$

1. $a$
2. $b$
3. $c$

Q. The most appropriate option for the following sets
$A$ is set of letters of the word 'debit card'
$B$ is the set of letters of the word 'bad credit'

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are unequal sets
3. $A$ and $B$ are disjoint sets
4. $A$ and $B$ are identical sets

Q. Match the following

$$\begin{array}{cc}\text{Column A}& \text{Column B}\\ 1.A=\{x:x\text{is an odd natural number}\}& a.\{\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{3}{4},\frac{3}{5},\frac{5}{7}\}\\ 2.B=\{x:x=(n^2)\},n\in N\text{and}x<100& b.\{1,4,9,16,25,........10000\}\\ 3.C=\{x:x=\frac{n}{n+2},\text{where}n\text{is a natural number and}1\le n\le 6\}& c.\{1,4,9,16,25,36,49,64,81\}\\ 4.D=\{x:x\text{is a letter of the word TRIGONOMETRY}\}& d.\{G,E,I,M,N,O,R,T,Y\}\\ & e.\{1,3,5,7,9,...............\}\end{array}$$

1. 1 - e, 2 - b, 3 - a, 4 - d

2. 1 - e, 2 - c, 3 - a, 4 - d

3. 1 - c, 2 - b, 3 - a, 4 - d

4. 1 - c, 2 - b, 3 - d, 4 - e