Discrete Mathematics Answers

(i). In MA161 class, the lecturer gave the following proposition. Let A (x, y) be “ y is greater than or equal to x ”. The domain for the proposition is the set of nonnegative integers. The students were tasked to determine what are the truth values of ∃y ∀xA (x,y) and ∀x∃yA(x,y ) ?

determine whether these functions are bijections f:Q to R x²+1/x

For n∈Z, prove n^2 is odd if and only if n is odd.

Prove: If ab is even then a or b is even.

Prove: There is no positive integer n such that n^2+n^3=100.

Determine if the statement is TRUE or FALSE. Justify your answer. All numbers under discussion are integers.

1.For each m ≥  1 and n ≥ 1, if mn is a multiple of 4, then m or n is a

multiple of 4.

2. For each m ≥ 1 and n ≥ 1, if mn is a multiple of 3, then m or n is a

multiple of 3.

Determine whether the relation R on the set of all real

numbers is reflexive, symmetric, antisymmetric, and/or

transitive, where (x, y) ∈ R if and only if

a) x + y = 0.

b) x = ±y.

c) x - y is a rational number.

By using principle of mathematical induction prove 2^n > n^2

if n is an integer greater than 4.