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A function $f :\left \{ 0,1 \right \}^{n}\rightarrow \left \{ 0,1 \right \}$ is called symmetric if for every $X_{1},X_{2},X_{3}.....X_{n}$  $\epsilon$ $\left \{ 0,1 \right \}$and every permutation $\sigma$ of $[1,2,3,4 ..... ,n] $ we have $f(x_{1},x_{2},.......,x_{n}) = f(x_{\sigma(1)}, x_{\sigma(2)},.....x_{\sigma(n)}$)

The number of such symmetric funtion is

a) $2^{n+1}$

b) $2^n$

c)$\frac{2^{2^{n}}}{n!}$

d) $2^{2^{n}}$

e) $n!$
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