Discrete Mathematics Answers

Give an example of relation which is Reflexive, anti symmetric & transitive but not symmetric

Show that p > q and (p A q) V (-p ^ ¬q are logically equivalent.

Determine whether each of the following statements is a proposition or not. If it is, give its truth value.

p: Mindanao is an island in the Philippines.

q: Find a number which divides your age.

r: My seatmate will get a perfect score in the Logic exam.

s: Welcome to the Philippines!

If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.

If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.

Find the bitwise OR, bitwise AND, and bitwise XOR of each of these pairs of bit strings. a) 101 1110, 010 0001

b) 1111 0000, 1010 1010

pc) 00 0111 0001, 10 0100 1000

d) 11 1111 1111, 00 0000 0000

Let p = “The Exams are decided” and q = “The Papers have been set”

Express each of these compound propositions as English sentences. And state

whether it is Contradiction, Tautology or Contingency.

a) ¬ p :

b) p ∨ q :

c) q → p :

d) p ↔ q :

e) ¬ p ∧ q :

f) ¬ p → ¬ q :

g) ¬ q → ¬ p :

h) ¬ q ∨ (¬ p ∧ q) :

If t is a tautology and c is contradiction, show that p ∨ t ≡ p and p ∧ c ≡ c?

Show that ¬P → (Q → R) and Q→(P∨R) are logically equivalent.