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We have already introduced the symbols -p (for negation "not p") and pVq (for disjunction "either p or q"). We now introduce the symbol A for conjunction and call the formula of sentential logic (pAq) the conjunction of p and q with the following truth table: Р 1 1 0 0 q (p^g) 1 1 0 0 0 Part (b) ((p →q) → p) 0 1 0 Next we introduce another symbol → called the conditional. The formula of sentential logic (p→q) is read as "if p, then q" or "q if p" or "p only if q". It has the following truth table: Р q (p→g) 1 1 1 1 0 0 1 0 0 0 1 1 Using truth tables determine the truth functions of the following formulas. Hint: What is the main connective? Part (a) (p¬q)

We have already introduced the symbols -p (for negation "not p") and pVq (for disjunction "either p or q"). We now introduce the symbol A for conjunction and call the formula of sentential logic (pAq) the conjunction of p and q with the following truth table: Р 1 1 0 0 q (p^g) 1 1 0 0 0 Part (b) ((p →q) → p) 0 1 0 Next we introduce another symbol → called the conditional. The formula of sentential logic (p→q) is read as "if p, then q" or "q if p" or "p only if q". It has the following truth table: Р q (p→g) 1 1 1 1 0 0 1 0 0 0 1 1 Using truth tables determine the truth functions of the following formulas. Hint: What is the main connective? Part (a) (p¬q)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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We have already introduced the symbols -p (for negation "not p") and pVq (for disjunction "either p or q"). We now introduce the symbol A for conjunction and call the formula of sentential logic (p^q) the conjunction of p and q with the following truth table: Р 1 1 0 0 Part (b) ((p →q) → p) 9 1 0 1 0 Next we introduce another symbol → called the conditional. The formula of sentential logic (p→q) is read as "if p, then q" or "q if p" or "p only if q". It has the following truth table: Р q 1 1 1 0 0 (p^g) 1 0 0 0 0 1 1 Using truth tables determine the truth functions of the following formulas. Hint: What is the main connective? Part (a) (p^¬q) 010 (p→g) 1
Transcribed Image Text:We have already introduced the symbols -p (for negation "not p") and pVq (for disjunction "either p or q"). We now introduce the symbol A for conjunction and call the formula of sentential logic (p^q) the conjunction of p and q with the following truth table: Р 1 1 0 0 Part (b) ((p →q) → p) 9 1 0 1 0 Next we introduce another symbol → called the conditional. The formula of sentential logic (p→q) is read as "if p, then q" or "q if p" or "p only if q". It has the following truth table: Р q 1 1 1 0 0 (p^g) 1 0 0 0 0 1 1 Using truth tables determine the truth functions of the following formulas. Hint: What is the main connective? Part (a) (p^¬q) 010 (p→g) 1
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