CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
If a set A has 4 elements, how many different relations can be defined on A (that is, subsets of A × A)?
There are 65536 relations on a 4-element set. A × A contains 16 ordered pairs, and every subset of these 16 pairs is a relation, giving 2 raised to the power 16, which equals 65536.
- A16
- B256
- C1024
- D65536Correct
Explanation
A × A has 4 × 4 = 16 ordered pairs. Each relation is a subset of A × A, so the number of relations is 2^16 = 65536. The value 256 comes from wrongly using 2^8, and 16 counts only the pairs themselves.
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