Discrete Mathematics Answers

Briefly discuss and illustrate the different ways to represent relations

Let Q (x,) be the statement “the word x contains the letter a.” What are the truth values of the following?

a) P(orange)

b) P(lemon)

c) P(true)  

d) P(false) 

1.    Determine whether this proposition is a tautology.

[(p → q) ∧ (q → r)] → (p→ r) 

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