Question 1

1. If (x + 2, 4) = (5, y - 1), find the values of x and y.

A) x=7, y=3B) x=3, y=5C) x=3, y=3D) x=5, y=5

Answer

✓ Correct Answer: Option B

Question 2

2. If set A has 3 elements and set B has 4 elements, how many elements are in $A \times B$?

A) 12B) 7C) $2^{12}$D) 1

Question 3

3. A relation R from set A to set B is mathematically defined as:

A) $R = A \cup B$B) $R = A \cap B$C) $R \subseteq A \times B$D) $R \supseteq A \times B$

Answer

✓ Correct Answer: Option C

Explanation: Hint: By definition, a relation is a subset of the Cartesian product.

Question 4

4. Find the domain of the relation R = \{(1, 2), (3, 4), (5, 6)\}.

A) \{1, 3, 5\}B) \{2, 4, 6\}C) \{1, 2, 3, 4, 5, 6\}D) \emptyset

Answer

✓ Correct Answer: Option A

Explanation: Hint: Domain is the set of all first elements of the ordered pairs in R.

Question 5

5. Find the range of the relation $R = \{(x, y) : y = x + 5; x \in \{1, 2, 3\}\}$.

A) \{1, 2, 3\}B) \{6, 7, 8\}C) \{5, 10, 15\}D) \{0, 5, 10\}

Answer

✓ Correct Answer: Option B

Explanation: Hint: Substitute x values into y = x+5 to get the set of second elements.

Question 6

6. If n(A) = p and n(B) = q, what is the total number of relations that can be defined from A to B?

A) pqB) $p^q$C) $q^p$D) $2^{pq}$

Answer

✓ Correct Answer: Option D

Explanation: Hint: The number of relations is the number of subsets of $A \times B$.

Question 7

7. Let A = \{1, 2\}. The identity relation $I_A$ on set A is:

A) \{(1, 2), (2, 1)\}B) \{(1, 1), (2, 2), (1, 2)\}C) \{(1, 1), (2, 2)\}D) \emptyset

Answer

✓ Correct Answer: Option C

Explanation: Hint: Identity relation contains only pairs where the first and second elements are the same for every element in A.

Question 8

8. If R is a relation from A to B, then the inverse relation $R^{-1}$ is a relation from:

A) B to AB) A to AC) B to BD) $A \times B$ to \emptyset

Answer

✓ Correct Answer: Option A

Question 9

9. If R = \{(1, 2), (2, 3)\}, then $R^{-1}$ is:

A) \{(1, 2), (2, 3)\}B) \{(2, 1), (3, 2)\}C) \{(1, 1), (2, 2)\}D) \{(3, 2), (2, 1), (1, 1)\}

Answer

✓ Correct Answer: Option B

Question 10

10. The set of all second elements of the ordered pairs in a relation R from A to B is called the:

A) DomainB) CodomainC) RangeD) Cartesian Product

Answer

✓ Correct Answer: Option C

Explanation: Hint: Domain is the 1st elements, Range is the 2nd elements.

Question 11

11. If A = \{a, b\}, how many relations can be defined on set A?

A) 4B) 16C) 8D) 2

Answer

✓ Correct Answer: Option B

Explanation: Hint: Number of relations on set A is $2^{n(A) \times n(A)} = 2^{2 \times 2}$.

Question 12

12. If $(x, 1) \in \{(2, 1), (3, 4)\}$, then the value of x is:

A) 1B) 3C) 4D) 2

Answer

✓ Correct Answer: Option D

Explanation: Hint: Look for the ordered pair where the second element is 1.

Question 13

13. The smallest relation on any non-empty set A is the:

A) Empty relation \emptysetB) Identity relationC) Universal relationD) Singleton relation

Answer

✓ Correct Answer: Option A

Explanation: Hint: The empty set is a subset of every set, including the Cartesian product.

Question 14

14. If R is a relation from A to B, and B = \{1, 2, 3\}, then the Codomain of R is:

A) The Range of RB) The Domain of RC) The set BD) The set A

Answer

✓ Correct Answer: Option C

Explanation: Hint: For a relation from A to B, the entire set B is the codomain.

Question 15

15. Let A = \{1, 2\} and B = \{3, 4\}. Which of the following is NOT a relation from A to B?

A) \{(1, 3), (2, 4)\}B) \{(3, 1), (4, 2)\}C) \{(1, 4)\}D) \emptyset

Answer

✓ Correct Answer: Option B

Explanation: Hint: Elements of a relation from A to B must be of form (a, b) where $a \in A$ and $b \in B$.

Question 16

16. If $n(A \times B) = 15$ and n(A) = 3, find n(B).

A) 5B) 12C) 45D) 18

Answer

✓ Correct Answer: Option A

Question 17

17. If $R = \{(x, y) : x^2 + y^2 = 0\}$ on the set of real numbers, then R is:

A) \{(1, -1)\}B) \{(1, 1)\}C) \{(0, 0)\}D) \emptyset

Answer

✓ Correct Answer: Option C

Explanation: Hint: For real numbers, $x^2 + y^2 = 0$ only when both x and y are zero.

Question 18

18. If $A \times B = \emptyset$, it implies:

A) A is not emptyB) B is not emptyC) Both A and B are infiniteD) At least one of A or B is an empty set

Answer

✓ Correct Answer: Option D

Explanation: Hint: Cartesian product is empty if either set has no elements to pair.

Question 19

19. Let $R = \{(x, y) : y = x^2\}$. If $(3, k) \in R$, what is the value of k?

A) 6B) 9C) 3D) 27

Answer

✓ Correct Answer: Option B

Question 20

20. Range of a relation is always a subset of the:

A) CodomainB) DomainC) Set AD) None of these

Answer

✓ Correct Answer: Option A

Explanation: Hint: The Range consists of actual outputs, while Codomain is the set of all possible outputs.

Grade 11 : Mathematics - Relations (Set 1)

1. If (x + 2, 4) = (5, y - 1), find the values of x and y.

2. If set A has 3 elements and set B has 4 elements, how many elements are in $A \times B$?

3. A relation R from set A to set B is mathematically defined as:

4. Find the domain of the relation R = \{(1, 2), (3, 4), (5, 6)\}.

5. Find the range of the relation $R = \{(x, y) : y = x + 5; x \in \{1, 2, 3\}\}$.

6. If n(A) = p and n(B) = q, what is the total number of relations that can be defined from A to B?

7. Let A = \{1, 2\}. The identity relation $I_A$ on set A is:

8. If R is a relation from A to B, then the inverse relation $R^{-1}$ is a relation from:

9. If R = \{(1, 2), (2, 3)\}, then $R^{-1}$ is:

10. The set of all second elements of the ordered pairs in a relation R from A to B is called the:

11. If A = \{a, b\}, how many relations can be defined on set A?

12. If $(x, 1) \in \{(2, 1), (3, 4)\}$, then the value of x is:

13. The smallest relation on any non-empty set A is the:

14. If R is a relation from A to B, and B = \{1, 2, 3\}, then the Codomain of R is:

15. Let A = \{1, 2\} and B = \{3, 4\}. Which of the following is NOT a relation from A to B?

16. If $n(A \times B) = 15$ and n(A) = 3, find n(B).

17. If $R = \{(x, y) : x^2 + y^2 = 0\}$ on the set of real numbers, then R is:

18. If $A \times B = \emptyset$, it implies:

19. Let $R = \{(x, y) : y = x^2\}$. If $(3, k) \in R$, what is the value of k?

20. Range of a relation is always a subset of the: