Discrete Mathematics Answers

​ For the function f defined by f(n) =n2+ 1/n+ 1 for n∈N, show that f(n)∈Θ(n). Use

Each of the following numbers represents a signed decimal number in the 2’s complement system. Determine the decimal value in each case

 10011001

 11101

 01111011

The recursive definition of a function X is given as:
f(0)=5 and f(n)=f(n-2)+5
Now, find out the value of f(14) using the above function.

Among the integer 1 to 300,find how many are not divisible by 3,nor by 5 also find how many are divisible by 3but not by 7

Consider the relation on the set of integer R={(a, b) /a=b+1} check whether it is equivalence relation

The recursive definition of a function X is given as:
f(0)=5 and f(n)=f(n-2)+5
Now, find out the value of f(14) using the above function.

Explain graph isomorphism with proper diagrams.

6. Select the statement that is the negation of “You wear matching socks to the interview or you don’t get
hired.”
A. You don’t wear matching socks to the interview or you get hired.
B. You don’t wear matching socks to the interview and you get hired.
C. You don’t wear matching socks to the interview and you don’t get hired.
D. If you don’t wear matching socks to the interview, then you don’t get hired.

7-13: Find the Truth Value (show your solution)
7. Suppose p is false, q is false, s is true. Find the truth value of (s ∨ p) ∧ (q∧ ┐s)
8. Suppose p is true, q is true, r is false, s is false. Find the truth value of (s ∨ p) ∧ (┐r ∨ ┐s)
9. Suppose p is true, q is true, s is false. Find the truth value of (┐s ∨ p) ∨ (q ∧ ┐s)
10. Suppose p is false, s is false, r is true. Find the truth value of ┐ [(s ∧ p) ∨ ┐r]
11. Suppose p is false, q is true, s is true. Find the truth value of (p ∧ ┐q) ∨ ┐s
12. Suppose p is false, q is true, r is false. Find the truth value of (p ∨ ┐q) ∨ r
13. Suppose p is true, q is true, r is true, s is false. Find the truth value of (┐p ∨ s) ∨ (s ∧ r)
14-15: Make a truth table for the given expression.
14. (┐p ∧ q) ∨ (p ∧ ┐q)
15. (┐p ∧ q) (┐p ∨ q)