Discrete Mathematics Answers

Determine whether this proposition is a tautology.

[(p → q) Ù (q → r)] → (p→ r) 

What is the value of this statement -B if B = F.

A. True

B. False

What is the value of this statement -(B VC) if B=F.C=T.

A. True

B. False

What is the value of this implication p→qif p = F and q = F.

A. True

B. False

Define permutation function and find out all permutation on the set S = {𝑎, 𝑏, 𝑐}

Determine whether each of the function from 𝑍 to Z is onto

(a) 𝑓(𝑛) = 𝑛³

(b) 𝑓(𝑛) = 𝑛² − 1

Determine whether each of the function from 𝑍 to Z is one to one

(a) 𝑓(𝑛) = 𝑛 − 1

(b) 𝑓(𝑛) = 𝑛² + 1

Let 𝐴 and 𝐵 be sets such that 𝐴 ∪ 𝐵 ⊆ 𝐵 and 𝐵 ⊆ 𝐴 . Draw the corresponding Venn

diagram

Show, by the use of the truth table (truth matrix), that are ¬(P∨(Q∨(¬P→¬R))) and ¬P(Q→R) logically equivalent. (15 points)

Show, by the use of the truth table (truth matrix), that the (p ∨ q) ∨ [(¬p) ∧ (¬q)] is a contradiction. 

1. Let p and q be the propositions.

p: It is below freezing.

q: It is snowing.

Express each of these propositions in complete English sentences.

a) p ∧ q 

b) p ∧ ¬q 

c) ¬p ∧ ¬q 

d) q ∨ p 

e) p → q 

f) q ∧ ¬p 

g) q → p 

2. Solve the following.

a) Construct a truth table.

¬p ∧ ( p ↔ ¬q )

b) Construct a truth table.

p → ( q ∧ r )

c) Construct a truth table.

( p → q ) ∨ ( ¬p ↔ r )

d) Find out if the following is a tautology, contradiction, or contingency

( p ∨ q ) ∧ ( ¬p ∧ ¬q )

e) Find out if the following propositions have logical equivalence.

( p ↔ q ) ≡ ( p → q ) ∧ ( q → p )