If there are 62 onto mapping from a set X containing n elements to the set Y={−1,1}, then n is equal to

# If there are 62 onto mapping from a set X containing n elements to the set $Y=\left\{-1,1\right\}$, then $n$ is equal to

1. A

4

2. B

5

3. C

6

4. D

7

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### Solution:

Let $X=\left\{{x}_{1},{x}_{2},\dots ,{x}_{\mathrm{n}}\right\}$

Each ${x}_{i}$ can have two images  and 1. Thus, there are ${2}^{n}$ mappings from $X$ to $Y$.

But there are exactly two map ping which are not onto.

These are when all the elements are mapped to – 1 or when all the elements are mapped to 1.

$\therefore$there are ${2}^{n}-2$ onto mapping from $X$ to $Y$

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