Discrete Mathematics Answers

Draw the composite table for the operation * defined by x*y = x,

for every x , y ϵ S = {a, b, c, d}

Use a truth table to determine whether the given statement is a tautology or self-contradiction.

1. ~[p ∧ ( ~p v q)] v q

2. [p ∧ ( ~p v q)] v q

 (p ∧ r ∧ t) ↔ (q ∧ t) 

The set S consists of all integers from 1 to 2007 inclusive. For how many

elements n in S is f(n)=2n³+n²-n-2 over n²-2 an integer?

If U = {0,1,2,3,4,5,6,7,8,9}, A = {3,6,9} and B = {4,8}, find:

a. A _{intersection B}

_{b. A union B}

_{c. A complement}

_{d. B complement}

_{e. (A union B)complement}

Principle of mathematical induction to prove 1+2+2²+2³+....+2^n-1=2^n-1

Given A =

{1, 2, 3, 4} and B = {x, y, z}. Let R be the following relation from A to B

R = {(1, y), (1, z), (3, y), (4, x), (4, z)}

a. Determine the matrix of the relation

b. Draw the arrow diagram of R

c. Find the inverse relation R^-1of R

d. Determine the domain

and range of R