Discrete Mathematics Answers

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

Show that ¬(p ⊕ q) and p ↔ q are logically equivalent

Construct a truth table for each of these compound propositions.

a) p ∧ ¬p

b) p ∨ ¬p

c) (p ∨ ¬q) → q

d) (p ∨ q) → (p ∧ q)

e) (p → q) ↔ (¬q → ¬p)

f) (p → q) → (q → p)

Find all primes less than a specified positive integer n. (let’s say n =100).

(¬p→r) ∧ (q ↔p)

Use set builder notation to give a description of each of these sets.

a) {3, 6, 9, 12}

b) {−4,−3,−2,−1, 0, 1, 2, 3, −4}

p ∧¬q

Example 1:

Let P, Q and R be the propositions

P: It’s raining outside.

Q: It’s safe to drive.

R: The roads are slippery.

a)      Though it’s raining outside but the roads are not slippery.

b)     It’s safe to drive if and only if the roads are not slippery:

c)      If it’s raining outside and the roads are not slippery then it’s safe to drive.

d)     Driving is safe after the rain stopped if and only if the roads are not slippery.

Using the handshaking principle,determine the number edges of a graph with fourteen vertices and each with degree six

How many bit strings of length 11 have more 0s than 1s?