Discussion
Let \(X = \{1, 2, 3, 4, 5, 6, 7\}\) . Let \(R = \{(1, 1), (1, 2), (1, 3), (5, 6), (6, 7), (7, 5)\}\) be a relation on X. Then the relation R will become reflexive if we include the pairs
Answer: E
R becomes reflexive on adding (2,2), (3,3), (4,4), (5,5), (6,6) and (7,7).
A relation on X is reflexive when \((x, x) \in R\) for every \(x \in X\). R already contains (1,1) but none of (2,2) to (7,7), so all six must be added.
The other options each fail somewhere: one swaps (2,2) for (2,7), one replaces (4,4) with (4,3), one has (7,6) instead of (7,7), and one leaves out (4,4) and (6,6). Pairs such as (2,7) or (4,3) do not help, since only pairs of the form \((x, x)\) count.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development