CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
A relation R is defined on the set of natural numbers as R = {(x, y) : x divides y}. Which of the following ordered pairs does NOT belong to R?
The ordered pair (6, 35) does not belong to R because 6 does not divide 35 evenly. For a pair (x, y) to satisfy the divisibility relation, x must divide y with no remainder, which is not true for 6 and 35.
- A(3, 12)
- B(5, 25)
- C(7, 42)
- D(6, 35)Correct
Explanation
For an ordered pair (x, y) to belong to R, x must divide y evenly. (3, 12): 12 ÷ 3 = 4 ✓; (5, 25): 25 ÷ 5 = 5 ✓; (7, 42): 42 ÷ 7 = 6 ✓; (6, 35): 35 ÷ 6 = 5.833... ✗. Since 6 does not divide 35, (6, 35) does not belong to R.
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