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KCET · Maths · Sets and Relations

Let R be the relation in the set \(\mathbb{N}\) given by \(R = \{(a, b) : a = b - 2, b > 6\}\). Which of the following is the correct answer?

  1. A \((2, 4) \in R\)
  2. B \((3, 8) \in R\)
  3. C \((6, 8) \in R\)
  4. D \((8, 7) \in R\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((6, 8) \in R\)

Step-by-step Solution

Detailed explanation

Given relation \(R = \{(a, b) : a = b - 2, b > 6\}\) on the set of natural numbers \(\mathbb{N}\).

For \((2, 4)\), \(b = 4\) which is not greater than \(6\). Thus, \((2, 4) \notin R\).

For \((3, 8)\), \(b = 8 > 6\) but \(a = 3 \neq 8 - 2\). Thus, \((3, 8) \notin R\).

For \((6, 8)\), \(b = 8 > 6\) and \(a = 6 = 8 - 2\). Thus, \((6, 8) \in R\).

For \((8, 7)\), \(b = 7 > 6\) but \(a = 8 \neq 7 - 2\). Thus, \((8, 7) \notin R\).

Answer: \((6, 8) \in R\)