10th Maths Unit 1: Relations and Functions Exercise 1.1 Solutions | Cartesian Product

10th Mathematics : UNIT 1 : Relation and Function : Exercise 1.1: Cartesian Product Solutions

Exercise 1.1: Cartesian Product - Solutions

Maths Book back answers and solution for Exercise questions - Mathematics : Relation and Function: Cartesian Product: Exercise Questions with Answer, Solution

Question 1

Find \(A \times B\) , \(A \times A\) and \(B \times A\)

(i) \(A = \{2, -2, 3\}\) and \(B = \{1, -4\}\)

(ii) \(A = B = \{p, q\}\)

(iii) \(A = \{m, n\}\) ; \(B = \emptyset\)

Solution:

Solution for Question 1

Question 2

Let \(A = \{1,2,3\}\) and \(B = \{x | x\) is a prime number less than 10}. Find \(A \times B\) and \(B \times A\).

Solution:

Solution for Question 2

Question 3

If \(B \times A = \{(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)\}\) find A and B.

Solution:

Solution for Question 3

Question 4

If \(A = \{5, 6\}\) , \(B = \{4, 5, 6\}\) , \(C = \{5, 6, 7\}\) , Show that \(A \times A = (B \times B) \cap (C \times C)\) .

Solution:

Solution for Question 4

Question 5

Given A={1,2,3}, \(B = \{2,3,5\}\), \(C = \{3,4\}\) and \(D = \{1,3,5\}\), check if \((A \cap C) \times (B \cap D) = (A \times B) \cap (C \times D)\) is true?

Solution:

Solution for Question 5

Question 6

Let \(A = \{x \in W | x < 2\}\) , \(B = \{x \in N | 1 < x \le 4\}\) and \(C = \{3, 5\}\). Verify that

(i) \(A \times (B \cup C) = (A \times B) \cup (A \times C)\)

(ii) \(A \times (B \cap C) = (A \times B) \cap (A \times C)\)

(iii) \((A \cup B) \times C = (A \times C) \cup (B \times C)\)

Solution:

Solution for Question 6

Question 7

Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that

(i) \((A \cap B) \times C = (A \times C) \cap (B \times C)\)

(ii) \(A \times (B - C) = (A \times B) - (A \times C)\)

Solution:

Solution for Question 7

Final Answers

  • 1. (i) \(A \times B = \{(2, 1), (2, -4), (-2, 1), (-2, -4), (3, 1), (3, -4)\}\)
    \(A \times A = \{(2, 2), (2, -2), (2, 3), (-2, 2), (-2, -2), (-2, 3), (3, 2), (3, -2), (3, 3)\}\)
    \(B \times A = \{(1, 2), (1, -2), (1, 3), (-4, 2), (-4, -2), (-4, 3)\}\)
  • 1. (ii) \(A \times B = \{(p, p), (p, q), (q, p), (q, q)\}\)
    \(A \times A = \{(p, p), (p, q), (q, p), (q, q)\}\)
    \(B \times A = \{(p, p), (p, q), (q, p), (q, q)\}\)
  • 1. (iii) \(A \times B = \{\}\)
    \(A \times A = \{(m, m), (m, n), (n, m), (n, n)\}\)
    \(B \times A = \{\}\)
  • 2. \(A \times B = \{(1, 2), (1, 3), (1, 5), (1, 7), (2, 2), (2, 3), (2, 5), (2, 7), (3, 2), (3, 3), (3, 5), (3, 7)\}\)
    \(B \times A = \{(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (5, 1), (5, 2), (5, 3), (7, 1), (7, 2), (7, 3)\}\)
  • 3. \(A = \{3, 4\}\) and \(B = \{-2, 0, 3\}\)
  • 5. True
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