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# Problem set

Question 1

Consider the functions f(x) = x^2 and g(x) = square root of x, both with domain and co-domain R+, the set of positive real numbers. Are f and g inverse functions? Give a brief reason.

Question 2

Given the Hamming distance function f: A X A -> Z defined on pairs of 8-bit strings, (where A is the set of 8-bit strings) select which of the following are correct (select
zero or more).

a. f is one-to-one
b. f has range {0, 1, 2, 3, 4, 5, 6, 7, 8}.
c. f is onto
d. f is invertible.

Question 3

Suppose set A = {0, 1, 3} and B = {2,4,6} in a universe U = {0,1,2,3,4,5,6,7}. Match the set names on the left with their membership lists on the right: I use ^ for intersection, u for union, ' for complement.

MATCH THE FOLLOWING.

AuB'
(AuB)'
P(A)
(A^B)'
A^A'

a. {0,1,3,5,7}
b. {5,7}
c. { {}, {0},{1},{3}, {0,1}, {1,3}, {0,3}, {0,1,3}}
d. {0,1,2,3,4,5,6,7}
e. {}

Question 4

Select the true statements, but no false statements, in the following list. Notation: {} is the empty set, relations like set membership are spelled out in words. There may be zero or more true statements.

a. For all sets A and B, if A is a subset of B, then A intersection B' (A^B') = {}.
b. For every set B, {} is a subset of B.
c. For all sets B, {} intersection B = B.
d. For all sets B, {} union B = B.
e. For every set B, {} is an element of B.

#### Solution Summary

This solution is comprised of a detailed explanation to answer are f and g inverse functions.

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