Discrete Mathematics Answers

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.

Use set builder notation to give a description of each of these sets. a) {0, 3, 6, 9, 12} b) {−3,−2,−1, 0, 1, 2, 3} c) {m, n, o, p}

Use a Venn diagram to illustrate the subset of even integers in the set of all positive integers not exceeding 15.

let a and b be sets. show that (a∩b)⊆a

1. Show that ¬p → (q + r) and q→ (p V r) are logically equivalent.
2. show, by the use of the truth table (truth matrix), that the (p v q)v[(p¬)ʌ(q)] is a contradiction.