Discrete Mathematics Answers

 Let P(x), Q(x), and R(x) be the statements “x is a lion,” “x is fierce,” and “x drinks coffee,” respectively. Assuming that the domain consists of all creatures, express the statements in the argument using quantifiers and P(x), Q(x), and R(x).

“Some fierce creatures do not drink coffee.”

Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. a) ∃x(x2 = −1) b) ∀x(x2 + 2 ≥ 1)

Prove the following equivalences by the logical derivation: 

(b) (p ∧ q) → r ≡ (p → r) ∨ (q → r)

Translate the following sentences into propositional logic) If you do not do homework by yourself or copy from other places, then you will get 0 in homework.

Use set builder notation to give a description of these sets a. {0,3,6,9,12} b. {-3, -2, -1, 0 1 2 3} c.{m, n, o, p}

Use set builder notation to give a description of this set {0,3,6,9,12}

Let p,q and r be the following proposition

P:jun jun has a date with petra

Q:juan is sleeping

R:lance is eating

1.p v q

2.q 

V (～r)

3.p

V (q v r)

Let A = {a, b, c}, B = {x, y} and C = {0, 1}. Find a.      C x B x A b.      B x B x B