Quiz-A        

#1.-  (following Cantor) What are the fundamental concepts of Mathematics?

a) positive and negative numbers.

b) fear, uncertainty and doubt.

c) sets, elements and logic.

d) real numbers and real functions.

#2.- Let and let  be a function from Pto ℤ defined as: .

a) Is  one-to-one? if the answer is  “no” , Produce a “witness”.

No

Witness: {3} and {1,2}

b) Is  onto?

No

Witness: No element of P(A) maps to integer 100

#3.- Let : ℤ  ℤ be defined as

a) Is  one-to-one?

        No

Witness: g(1) = g(-1).

b) Is  onto?

No

Witness: there is no value of x for which g(x) = -4

#4.- According to the laws of logarithms

 logxa - logxb