CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let A = {1, 2, 3, 4}. What is the total number of reflexive relations that can be defined on A?
The number of reflexive relations is 4096. A×A has 16 pairs, 4 of which (the diagonal) must be included. The remaining 12 pairs can each be chosen or left out independently, giving 2^12 = 4096 reflexive relations.
- A16
- B256
- C4096Correct
- D65536
Explanation
A has 4 elements, so A×A has 16 pairs. A reflexive relation must contain the 4 diagonal pairs, leaving 12 pairs free to be included or not. Number = 2^12 = 4096. The value 2^16 = 65536 counts all relations, ignoring the reflexivity condition.
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