[PDF] SOLUTIONS TO TAKE HOME EXAM 1 MNF130, SPRING 2010 PDF underveis1-sol.pdf

Show that ¬(p ∨ ¬q) and q ∧ ¬p are logically equivalent by (a) using a truth table; (b) using logical equivalences SOLUTION: (a) Truth table: p q ¬q p ∨ ¬q ¬ (p

The proposition p ∨ ¬(p ∧ q) is also a tautology as the following the truth table Show that (p → q) ∧ (q → p) is logically equivalent to p ↔ q Solution 1 Show

[PDF] Section 12, selected answers Math 114 Discrete Mathematics

columns for ¬(p ∧ q) and ¬p ∨ ¬q are identical, therefore they're logically equivalent 12 Show that each implication in Exercise 10 is a tautol- ogy without using

[PDF] Chapter 1 Logic

LOGIC The conjunction of p and q (read: p and q) is the statement p ∧ q p and q p q ¬p ¬q p ∧ q ¬(p ∧ q) ¬p ∨ ¬q p ∨ q ¬(p ∨ q) ¬p ∧ ¬q 0 0 1 1 0 1 1 Formally, two statements s1 and s2 are logically equivalent if s1 ↔ s2 is a tautology For an example of using the Laws of Logic, we show that p ↔ q ⇔ ( p ∧ q)

[PDF] Logic, Proofs

p ∧ q “p and q” Disjunction p ∨ q “p or q (or both)” Exclusive Or p ⊕ q p → q “if p then q” Biconditional p ↔ q “p if and only if q” The truth value of a compound proposition Note that that two propositions A and B are logically equivalent

[PDF] logically equivalent

contradiction example: p → q ∨ ¬p 3 p ¬p ¬p ∨ p 0 1 1 1 0 1 p ¬p ¬p ∧ p 0 1 0 1 0 0 Two compound propositions, p and q, are logically equivalent if p ↔ q is a Example 1: proof by truth tables that p → q and ¬p ∨ q are logically

[PDF] 21 Logical Equivalence and Truth Tables - USNA

statement variables (such as p,q, and r) and logical connectives (such as ∼,∧, and ∨) that becomes a statement when actual statements are substituted for the

[PDF] Logical Equivalence - University of Hawaii System

proposition p ↔ q is a tautology ▫ Compound propositions p and q are logically F F F ▫ Show that ▫ ¬(p ∨ q) ≡ ¬p ∧ ¬q (De Morgan's law) ▫ p → q

[PDF] Chapter 1 - Foundations - Grove City College

Logic • Proposition • Notation • Negation 1Taken from Lewis Carroll 1 ∧ 2 ∨ 3 → 4 ↔ 5 We will follow the book's convention and [almost] always use a proposition, e g , ¬p ∧ q is equivalent to (¬p) ∧ q, as opposed to ¬(p ∧ q) Example 3 Show that p ≡ p ∨ (p ∧ q): p q p ∧ q p ∨ (p ∧ q) T T T F F T F F