JEE Main 2026 — Sets and Relations Question with Solution
JEE Main 2026 (23 January Shift 1)
Question
Let . Let R be a relation on A defined by if and only if . Let be the number of elements in R. Let m and n be the minimum number of elements required to be added in to make it reflexive and symmetric relations respectively. Then is equal to :
Choose an option
Show full solutionCorrect option: C
Correct answer
C33
Step-by-step explanation
Given and iff .
For : , all 7 elements valid (7 pairs).
For : , all 7 elements valid (7 pairs).
For : (5 pairs).
For : (3 pairs).
For : (1 pair).
For : no valid .
So .
For reflexive: . Already present for . Missing for , so .
For symmetric: need for every . Missing pairs: , so .
.
For : , all 7 elements valid (7 pairs).
For : , all 7 elements valid (7 pairs).
For : (5 pairs).
For : (3 pairs).
For : (1 pair).
For : no valid .
So .
For reflexive: . Already present for . Missing for , so .
For symmetric: need for every . Missing pairs: , so .
.
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