Function
Q11.
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a \in A. Which of the following statements is always true for all such functions f and g?Q12.
Let S denote the set of all functions f:{\{0,1\}}^{4} \rightarrow \{0,1\}. Denote by N the number of functions from S to the set {0,1}. The value of log_{2} log_{2}N is______.Q13.
Let : A\rightarrowB be injective (one-to-one) function. Define g:2^{A}\rightarrow 2^{B} as: g(C) = {f (x)| x \inC), for all subsets C of A. Defineg:2^{B}\rightarrow 2^{A} as : h(D) = {x | x \in A, f (x) \in D}, for all subsets D of B. Which of the following statements is always true?Q14.
Consider the set of all functions f:{0,1,...,2014}\rightarrow{0,1...,2014} such that f(f(i))=i, for 0\leqi\leq2014 . Consider the following statements. P. For each such function it must be the case that for every i, f(i) = i, Q. For each such function it must be the case that for some i,f(i) = i, R. Each such function must be onto. Which one of the following is CORRECT?Q18.
Let R denote the set of real numbers. Let f:R\times R \rightarrow R \times R be a bijective function defined by f(x,y) = (x+y, x-y). The inverse function of f is given by