Engineering-Mathematics
November 12, 2023OOPS
November 12, 2023Functions
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Question 7
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How many onto (or surjective) functions are there from an n-element (n ≥ 2) set to a 2-element set?
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2n
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2n-1
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2n-2
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2(2n– 2)
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Question 7 Explanation:
Onto function is possible if m ≥ n. So, no. of onto functions possible is,
nm – nC1 (n-1)m + nC2 (n-2)m + …….
Here in Question,
m = n, n = 2
So, the final answer will be,
= 2n – 2C1 (2-1)n + 2C2 (2-2)n
= 2n – 2 × 1 + 0
= 2n – 2
Correct Answer: C
Question 7 Explanation:
Onto function is possible if m ≥ n. So, no. of onto functions possible is,
nm – nC1 (n-1)m + nC2 (n-2)m + …….
Here in Question,
m = n, n = 2
So, the final answer will be,
= 2n – 2C1 (2-1)n + 2C2 (2-2)n
= 2n – 2 × 1 + 0
= 2n – 2