CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
If A has 3 elements and B has 4 elements, how many different relations can be defined from A to B?
The number of relations from A to B is 4096. A × B contains 3 × 4 = 12 ordered pairs, and each relation is a subset of A × B, so there are 2 raised to 12, which equals 4096, possible relations.
- A12
- B144
- C4096Correct
- D81
Explanation
A × B has 3 × 4 = 12 ordered pairs. Every subset of A × B is a relation, so the count is 2^12 = 4096. The option 144 comes from squaring 12 instead of using 2 to the power 12.
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