Question

A relation \(R\) is defined in the set \(N\) as \(R=\{(x,y):y=x+5,\,y>5\}\). Then which of the following is correct?

• A. \((6,10)\in R\)
• B. \((3,6)\in R\)
• C. \((4,9)\in R\)
• D. \((2,6)\in R\)

Hint:

Check y = x + 5 directly for each given pair.

Answer 1

The Correct Option is C

Step 1: Rewriting the rule:
\(R\) consists of every pair \((x,x+5)\) with \(x\in N\) (the condition \(y>5\) is automatic for \(x\ge1\)).

Step 2: Matching against the options:
We need the second coordinate to be exactly 5 more than the first. Testing (4,9): \(9-4=5\) ✓, matching no other option.

Final Answer:
\[ \boxed{(4,9)\in R} \]