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 relation \(R\) is defined in the set \(N\) as \(R=\{(x,y):y=x+5,\,y>5\}\). Then which of the following is correct?
Show Hint
Check y = x + 5 directly for each given pair.
Updated On: Sep 23, 2026
- \((6,10)\in R\)
- \((3,6)\in R\)
- \((4,9)\in R\)
- \((2,6)\in R\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Condition:
A pair \((x,y)\) is in \(R\) only if \(y=x+5\) (and automatically \(y>5\) then, since \(x\in N\)).
Step 2: Checking each option:
(6,10): \(6+5=11\neq10\) — fails. (3,6): \(3+5=8\neq6\) — fails. (4,9): \(4+5=9\) — holds! (2,6): \(2+5=7\neq6\) — fails.
Final Answer:
Only \((4,9)\) satisfies \(y=x+5\), and \(9>5\).\[ \boxed{(4,9)\in R} \]
A pair \((x,y)\) is in \(R\) only if \(y=x+5\) (and automatically \(y>5\) then, since \(x\in N\)).
Step 2: Checking each option:
(6,10): \(6+5=11\neq10\) — fails. (3,6): \(3+5=8\neq6\) — fails. (4,9): \(4+5=9\) — holds! (2,6): \(2+5=7\neq6\) — fails.
Final Answer:
Only \((4,9)\) satisfies \(y=x+5\), and \(9>5\).\[ \boxed{(4,9)\in R} \]
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