# Lecture - 1 Chapter 2 Relations and Functions

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NCERT EXERCISE 2.1 |

**Question 1.** If \(\left(\frac{x}{3}+1,y-\frac{2}{3}\right)=\left(\frac{5}{3},\frac{1}{3}\right) \), find the values of *x* and *y*.

**Question 2.** If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).

**Question 3.** If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

**Question 4.** State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.**(i).** If P = {*m*, *n*} and Q = {*n*, *m*}, then P × Q = {(*m*, *n*),(*n*, *m*)}.**(ii).** If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (*x*, *y*) such that *x* ∈ A and *y *∈ B.**(iii).** If A = {1, 2}, B = {3, 4}, then \( A\times \left (B \capphi \right)=\phi \) .

**Question 5.** If A = {–1, 1}, find A × A × A.

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**Question 6.** If \( A\times B=\left{\left(a, x\right),\left(a, y\right),\left(b, x\right),\left(b,y\right)\right} \). Find A and B.

**Question 7.** Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that**(i).** A×(B∩C) = (A×B) ∩ (A×C).**(ii).** A × C is a subset of B × D.

**Question 8.** Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

**Question 9.** Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (*x*, 1), (*y*, 2), (*z*, 1) are in A × B, find A and B, where *x*, *y* and *z* are distinct elements.

**Question 10.** The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A and the remaining elements of A × A.