CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let A = {1, 2, 3} and B = {a, b}. How many functions from A to B are onto (surjective)?
There are 6 onto functions. The total number of functions from a 3-element set to a 2-element set is 2³ = 8. Subtracting the two constant functions, which miss one element of B, leaves 6 functions that cover both elements.
- A8
- B6Correct
- C4
- D2
Explanation
Total functions from A to B = 2³ = 8. Those that are not onto are the two constant functions (all to a, or all to b). So onto functions = 8 − 2 = 6. The value 8 ignores the onto condition.
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