Discrete Mathematics Answers

Find all combinations of truth values for p, q and r for which the statement ¬p ↔ (q ∧ ¬(p → r)) is true.

Find these values.

a) ⌈ 3/4⌉

b) ⌊ 7/8⌋

c) ⌈−3/4⌉

d) ⌊−7/8⌋

e) ⌈3⌉

f ) ⌊−1⌋

g) ⌊ 1/2 + ⌈ 3/2⌉ ⌋

h) ⌊ 1/2 ⋅ ⌊ 5/2⌋ ⌋

Describe the Hasse Diagram for the divisibility of the set A = {1, 2, 3, 5, 6 10, 15, 30}

Describe the Hasse diagram for the divisibility of the set A={1,2,3,5,6,10,15,30}

Let 

L(x,y

) be the statement “xl loves y,” where the universe of discourse for both x and y consist of all people in the world. Express each of these quantifications in English.  (a)    

Every body loves somebody.

 (b)   

There is somebody whom everybody loves.

 (c) There is somebody whom Lynn does not love. 

How many rows appear in a truth table for each of these compound propositions?

p →¬p

Determine whether these biconditionals are true or false.

a) 2 + 2 = 4 if and only if 1 + 1 = 2.

Prove the 3√7 is irrational 

¬ (p Ʌ q) V ( p Ʌ r) truth table

Determine the truth value of each of the statement below if the domain consists of all real numbers.

∀x(2x > x)