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p: 10+6=15 Determine the truth value for the statement pv-p. Choose the correct truth value below. Opv-p is false. Opv-p is true.

p: 10+6=15 Determine the truth value for the statement pv-p. Choose the correct truth value below. Opv-p is false. Opv-p is true.

Advanced Engineering Mathematics
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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**Logical Reasoning and Truth Values** **Statement Definition:** Let \( p \) represent the following statement. \[ p: 10 + 6 = 15 \] **Task:** Determine the truth value for the statement \( p \vee \sim p \). **Options:** - \( p \vee \sim p \) is false. - \( p \vee \sim p \) is true. **Explanation:** In logical reasoning, \( p \) represents a proposition which can be either true or false. The notation \( \sim p \) denotes the negation of \( p \). The expression \( p \vee \sim p \) is a logical disjunction, meaning it is true if at least one of the components (\( p \) or \( \sim p \)) is true. Since a proposition and its negation together encompass all possibilities (either \( p \) is true or \( \sim p \) is true), the disjunction \( p \vee \sim p \) is always true, known as the law of excluded middle. Here, the specific statement \( p: 10 + 6 = 15 \) is true, but regardless of its truth value on its own, the expression \( p \vee \sim p \) is universally true.
Transcribed Image Text:**Logical Reasoning and Truth Values** **Statement Definition:** Let \( p \) represent the following statement. \[ p: 10 + 6 = 15 \] **Task:** Determine the truth value for the statement \( p \vee \sim p \). **Options:** - \( p \vee \sim p \) is false. - \( p \vee \sim p \) is true. **Explanation:** In logical reasoning, \( p \) represents a proposition which can be either true or false. The notation \( \sim p \) denotes the negation of \( p \). The expression \( p \vee \sim p \) is a logical disjunction, meaning it is true if at least one of the components (\( p \) or \( \sim p \)) is true. Since a proposition and its negation together encompass all possibilities (either \( p \) is true or \( \sim p \) is true), the disjunction \( p \vee \sim p \) is always true, known as the law of excluded middle. Here, the specific statement \( p: 10 + 6 = 15 \) is true, but regardless of its truth value on its own, the expression \( p \vee \sim p \) is universally true.
Expert Solution
Step 1

Remember the truth values of the following :

p \neg p
True False
False True

 

and 

 

p q p \vee q
True True True
True False True
False True True
False False False
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