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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The number of relations, defined on the set ${a,b,c,d}$, which are both reflexive and symmetric, is equal to:
Solution
Set has 4 elements → total pairs = $4 \times 4 = 16$
Reflexive condition:
All $(a,a), (b,b), (c,c), (d,d)$ must be present → fixed
Remaining pairs = $16 - 4 = 12$
Symmetric condition:
Pairs form symmetric pairs like:
$(a,b)$ with $(b,a)$ → 1 choice pair
Total such independent pairs = $\frac{12}{2} = 6$
Each pair → 2 choices (present or not)
Total relations:
$ = 2^6 = 64 $
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