We have said what it means for a formula F to be: (1) a tautology, (2) contradictory. That F is a tautology and that G is contradictory represent two extreme poles of the spectrum of truth values for formulas in sentential logic. Most formulas involving sentences in English are neither tautologies nor contradictory. So, call a formula F satisfiable or contingent if its truth function has value 1 under at least one truth value assignment to its component simple sentences. It follows that a formula F is unsatisfiable if its truth function has value 0 under every truth value assignment to its component simple sentences. Your task is to use truth tables to determine whether the following formulas are: tautologies, contradictory (unsatisfiable) or contingent (satisfiable). (a) p (b) (p ∧ q) (c) (p ∨ q) (d) ((p ∧ q) → (p ∨ q)) (e) ((p ∨ q) → (p ∧ q))
We have said what it means for a formula F to be: (1) a tautology, (2) contradictory. That F is a tautology and that G is contradictory represent two extreme poles of the spectrum of truth values for formulas in sentential logic. Most formulas involving sentences in English are neither tautologies nor contradictory. So, call a formula F satisfiable or contingent if its truth function has value 1 under at least one truth value assignment to its component simple sentences. It follows that a formula F is unsatisfiable if its truth function has value 0 under every truth value assignment to its component simple sentences. Your task is to use truth tables to determine whether the following formulas are: tautologies, contradictory (unsatisfiable) or contingent (satisfiable). (a) p (b) (p ∧ q) (c) (p ∨ q) (d) ((p ∧ q) → (p ∨ q)) (e) ((p ∨ q) → (p ∧ q))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
We have said what it means for a formula F to be: (1) a tautology, (2) contradictory. That F is a
tautology and that G is contradictory represent two extreme poles of the spectrum of truth values for formulas
in sentential logic. Most formulas involving sentences in English are neither tautologies nor contradictory.
So, call a formula F satisfiable or contingent if its truth function has value 1 under at least one truth value
assignment to its component simple sentences. It follows that a formula F is unsatisfiable if its truth function
has value 0 under every truth value assignment to its component simple sentences. Your task is to use
truth tables to determine whether the following formulas are: tautologies, contradictory (unsatisfiable) or
contingent (satisfiable).
(a) p
(b) (p ∧ q)
tautology and that G is contradictory represent two extreme poles of the spectrum of truth values for formulas
in sentential logic. Most formulas involving sentences in English are neither tautologies nor contradictory.
So, call a formula F satisfiable or contingent if its truth function has value 1 under at least one truth value
assignment to its component simple sentences. It follows that a formula F is unsatisfiable if its truth function
has value 0 under every truth value assignment to its component simple sentences. Your task is to use
truth tables to determine whether the following formulas are: tautologies, contradictory (unsatisfiable) or
contingent (satisfiable).
(a) p
(b) (p ∧ q)
(c) (p ∨ q)
(d) ((p ∧ q) → (p ∨ q))
(e) ((p ∨ q) → (p ∧ q))
(f) (¬¬p → p)
(d) ((p ∧ q) → (p ∨ q))
(e) ((p ∨ q) → (p ∧ q))
(f) (¬¬p → p)
(g) (p ∧ ¬p)
(h) (p → (q → p))
(i) ((p ∧ q) ∧ (¬p ∨ ¬q))
(j) ((p ∨ q) → (¬p ∧ ¬q))
(h) (p → (q → p))
(i) ((p ∧ q) ∧ (¬p ∨ ¬q))
(j) ((p ∨ q) → (¬p ∧ ¬q))
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