Assertion :Let $E = {1, 2, 3, 4}$ and $F = {a, b}$ . Then the number of onto functions from E to F is 14. Reason: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
In onto functions each image must be assigned at least one pre-image.
Now if we consider the images a and b as two different boxes, then four
distinct objects 1, 2, 3, and 4 (pre-images) can be distributed in
$2^{4} -^{2} C_{1} (2 - 1)^{4} = 14$ ways.
Hence, both statements are correct and statement 2 is correct explanation of statement 1.

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Assertion :Let E={1,2,3,4} and F={a,b}. Then the number of onto functions from E to F is 14. Reason: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty.

Assertion :Let $E = {1, 2, 3, 4}$ and $F = {a, b}$ . Then the number of onto functions from E to F is 14. Reason: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty.