Relation and Functions Lecture 1
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Part - 1

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\cap\phi\right)=\phi .

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

Relation and Functions Lecture 1
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Part - 2

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.​