Grade 11 : Mathematics - Relations (Set 7) | Concept of Maths

Question 1

Consider two sets A and B such that n(A) = 5, n(B) = 5, and they share exactly 3 elements in common ($n(A \cap B) = 3$). Determine the number of elements in the intersection of their Cartesian products, $(A \times B) \cap (B \times A)$.

Accepted Answer

C) 9 elements

Answer

A) 3 elements

Answer

B) 6 elements

Answer

D) 25 elements

Question 2

A relation R is defined on the set of whole numbers $\mathbb{W}$ by $R = \{(x, y) : x^2 + y^2 = 100, x, y \in \mathbb{W}\}$. What is the total number of ordered pairs in this relation?

Accepted Answer

B) 4

Answer

A) 3

Answer

C) 5

Answer

D) Infinity

Question 3

Let A = \{1, 2, 3\} and R be a relation on A defined by R = \{(x, y) : y = x + 1\}. Find the sum of all elements present in the Domain of R and the Range of R combined.

Accepted Answer

D) 8

Answer

A) 6

Answer

B) 12

Answer

C) 10

Question 4

The total number of non-empty relations from a set A to a set B is found to be 255. If n(A) = 2, what must be the cardinality of set B?

Accepted Answer

A) 4

Answer

B) 8

Answer

C) 128

Answer

D) 2

Question 5

If $R = \{(x, y) : x + 3y = 12, x, y \in \mathbb{N}\}$, find the Range of R.

Accepted Answer

C) \{1, 2, 3\}

Answer

A) \{1, 2, 3\}

Answer

B) \{3, 6, 9\}

Answer

D) \{1, 2, 3, 4\}

Question 6

Let A = \{m, n\} and B = \{1, 2, 3\}. How many distinct relations from A to B must contain the specific ordered pair (m, 1)?

Accepted Answer

B) 32

Answer

A) 64

Answer

C) 16

Answer

D) 2

Question 7

Determine the Range of the relation $R = \{(x, y) : y = |x - 1|, x \in \mathbb{Z}, |x| \le 2\}$.

Accepted Answer

A) \{0, 1, 2, 3\}

Answer

B) \{-2, -1, 0, 1, 2\}

Answer

C) \{1, 2, 3\}

Answer

D) \{0, 1, 2\}

Question 8

Let A = \{1, 2, 3, 4, 5\} and R be a relation on A defined by R = \{(a, b) : a \ divides  b\}. Which of the following is NOT an element of R?

Accepted Answer

C) (4, 2)

Answer

A) (2, 4)

Answer

B) (1, 5)

Answer

D) (3, 3)

Question 9

If a relation R from set A to B is given by R = \{(1, a), (2, b), (3, a)\}, find the inverse relation $R^{-1}$.

Accepted Answer

B) \{(a, 1), (b, 2), (a, 3)\}

Answer

A) \{(a, 1), (b, 2), (a, 1)\}

Answer

C) \{(1, a), (2, b), (3, a)\}

Answer

D) \{(a, 1), (b, 2), (3, a)\}

Question 10

The Cartesian product $A \times B$ contains 6 elements. Three of these elements are (1, 4), (2, 6), (3, 4). What is set B?

Accepted Answer

D) \{4, 6\}

Answer

A) \{1, 2, 3\}

Answer

B) \{4, 6, 1\}

Answer

C) \{1, 4, 6\}