Discrete Mathematics Answers

show that ~p --> (q --> r ) and q --> (p v r) are logically equivalent

List the members of this set: {x | x is the square of an integer and x < 50}

Value of 3^222mod11

Let P(x) denote the statement x > 3. What is the truth value of the quan-

tification ∃xP(x), where the domain consists of all real numbers?

Construct a truth table (truth matrix) for each of these compound proposition

1. p ∧ ~q
2. p → ~q
3. ( p ∨ q ) → ( p ∧ q)
4. ( p ∨ q ) → r
5. ( p ∨ q )∧ ~r

by using truth table (truth matrix), show that each statement is a tautology, contradictory or a contingent statement.

1. ~p ∧ q
2. ~(p ∨ q) → q
3. ~(~p ∧ q) ∨ q
4. ~p → (p → q)
5. ~p → (p ∨ q)

List the members of these sets.

a) {x | x is a real number such that x 2 = 1}

b) {x | x is a positive integer less than 12}

Show that each of these conditional statements is a tautology

by using truth tables.

a) [¬p ∧ (p ∨ q)] → q

b) [(p → q) ∧ (q → r)] → (p → r)

c) [p ∧ (p → q)] → q

d) [(p ∨ q) ∧ (p → r) ∧ (q → r)] → r

Show that ¬p→(q→r) and q→(p ∨ r) are logically equivalent

Make a venn diagram Suppose that 53 of the 55 Information Technology students of University of Northern Philippines are taking atleast one of the mathematics subjects Mathematics in the Modern World, Discrete Mathematics, and Data management. Also suppose that: 24 taking Mathematics in the Modern World, 26 taking Discrete Mathematics, and 20 taking Data Management, 5 taking Mathematics in the Modern World and Discrete Mathematics, 7 taking Mathematics in the Modern World and Data Management, 8 taking Discrete Mathematics and Data Management.

How many circular permutations are there given the numbers on the clock?