The attachment that is enclosed with this homework request is Discrete Mathematics work. I am befuddled by these questions. 

 

 

1. There is no one-to-one correspondence between the set of all positive integers and the set of all odd positive integers because the second set is a proper subset of the
first. (True or False)
n
2. The solution to the recurrence relation: T (n) 9T ( ) n 3
3
is… with T (0) T (1) 1 3. Given the recurrence relation
T (n) 4T (n / 2) n with T (0) 1, then T (n) 4. Given the recurrence relation
T (n) 4T (n / 2) n 2 with T (0) 1, then T (n) 5. What is the time complexity (in Θ –notation) in terms of n?
Sum = 0;
for ( i = 0 ; i < n ; i++ )
for ( j = 1 ; j < n4 ; j = 4*j )
sum++; 6. What is the time complexity (in Θ –notation) in terms of n?
sum = 0 ;
for ( i = n ; i ≥ 1; i = i/2 )
for ( j = 0 ; j < n4 ; j = j+2 )
sum++; Properties: (1) reflexive (2) symmetric (3) anti-symmetric (4) transitive
(5) equivalence relation (6) partially ordered
relation 1 2 3 4 5 6 0 The relation R on the set of all people
where aRb means that a is younger
than b no no yes yes no no 1 The relation R on the set of all real
function f:N→R+ where f R g if and
only if f(n) = O(g(n)) 2 The relation R on the set of all real
function f:N→R+ where f R g if and
only if f(n) = Θ(g(n))

Attachments:

• 1492751708-Assignment 5.pdf