Question 13 of 35intermediate🔧 ApplyShort Answer2 marks

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

Correct Answer

R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}

Exercise: EXERCISE 2.2 | Q: 3 | (Page 7)
For More Understanding

Explanation

To find the relation R in roster form, we need to find all ordered pairs (x, y) where x ∈ A, y ∈ B, and the difference x - y is an odd number. We check each element of A with each element of B systematically.

Solution Steps

  1. Step 1: For x = 1: (1-4) = -3 (odd), (1-6) = -5 (odd), (1-9) = -8 (even). So pairs are (1, 4), (1, 6).

  2. Step 2: For x = 2: (2-4) = -2 (even), (2-6) = -4 (even), (2-9) = -7 (odd). So pair is (2, 9).

  3. Step 3: For x = 3: (3-4) = -1 (odd), (3-6) = -3 (odd), (3-9) = -6 (even). So pairs are (3, 4), (3, 6).

  4. Step 4: For x = 5: (5-4) = 1 (odd), (5-6) = -1 (odd), (5-9) = -4 (even). So pairs are (5, 4), (5, 6).

  5. Step 5: Combining all pairs: R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}.

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