Question 13 of 33beginner🔧 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 6)
For More Understanding

Explanation

To write the relation in roster form, we need to find all ordered pairs (x, y) where x ∈ A, y ∈ B, and the difference x - y is odd. A difference is odd when one number is even and the other is odd. Since all elements of A are odd (1, 3, 5) except 2, and all elements of B are even (4, 6) except 9, we check each combination systematically.

Solution Steps

  1. Step 1: For x = 1 (odd): |1-4| = 3 (odd) ✓, |1-6| = 5 (odd) ✓, |1-9| = 8 (even) ✗ → Pairs: (1, 4), (1, 6)

  2. Step 2: For x = 2 (even): |2-4| = 2 (even) ✗, |2-6| = 4 (even) ✗, |2-9| = 7 (odd) ✓ → Pair: (2, 9)

  3. Step 3: For x = 3 (odd): |3-4| = 1 (odd) ✓, |3-6| = 3 (odd) ✓, |3-9| = 6 (even) ✗ → Pairs: (3, 4), (3, 6)

  4. Step 4: For x = 5 (odd): |5-4| = 1 (odd) ✓, |5-6| = 1 (odd) ✓, |5-9| = 4 (even) ✗ → Pairs: (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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