Relations and Functions Class 11 (Question Bank)

📝Relations and Functions

Q. Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine
(i) A × B 
(ii) B × A
(iii) Is A × B = B × A ? 
(iv) Is n (A × B) = n (B × A) ?

Q. Find `x` and `y` if:

(i) `(4x + 3, y) = (3x + 5, – 2)` 

(ii) `(x – y, x + y) = (6, 10)`

Q. If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, `a \in`A, `b \in` B, find the set of ordered pairs such that `'a'` is factor of `'b'` and `a < b`.

Q. If P = `{x : x < 3, x \in ℕ}`, Q = `{x : x \leq 2, x \in` 𝕎}. Find `(P \cup Q) × (P \cap Q)`.

Q. Let A = {1, 2, 3,...,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y `\in` A}. Write down its domain, codomain and range.

Q. Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural number less than 4; x, y `\in`ℕ}. Depict this relationship using roster form. Write down the domain and the range.

Q. A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x `\in` A, y `\in` B}. Write R in roster form.

Q. Determine the domain and range of the relation R defined by R = {(x, x + 5) : x `\in` {0, 1, 2, 3, 4, 5}}.

Q. Write the relation R = {(`x, x^3`) : x is a prime number less than 10} in roster form.