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What can you say about the truth value of the statement represented by P^-P (A) It's a tautology (B) Sometimes True (C) Always True The notation à means what? (A) The proper subset of A (B) The power set of A (C) The complement of A (D) The cardinality of A (D) Always False

What can you say about the truth value of the statement represented by P^-P (A) It's a tautology (B) Sometimes True (C) Always True The notation à means what? (A) The proper subset of A (B) The power set of A (C) The complement of A (D) The cardinality of A (D) Always False

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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### Discrete Mathematics Multiple-Choice Questions #### Question 3: What can you say about the truth value of the statement represented by \( p \wedge \neg p \)? - (A) It's a tautology - (B) Sometimes True - (C) Always True - (D) Always False #### Question 4: The notation \(\overline{A}\) means what? - (A) The proper subset of \( A \) - (B) The power set of \( A \) - (C) The complement of \( A \) - (D) The cardinality of \( A \) #### Explanation: - **Question 3 Analysis**: This question involves logical operators. The expression \( p \wedge \neg p \) is a conjunction of \( p \) and its negation, which results in a contradiction and is thus always false. - **Question 4 Analysis**: The notation \(\overline{A}\) typically represents the complement of set \( A \), meaning all elements not in \( A \), assuming a universal set context is given.
Transcribed Image Text:### Discrete Mathematics Multiple-Choice Questions #### Question 3: What can you say about the truth value of the statement represented by \( p \wedge \neg p \)? - (A) It's a tautology - (B) Sometimes True - (C) Always True - (D) Always False #### Question 4: The notation \(\overline{A}\) means what? - (A) The proper subset of \( A \) - (B) The power set of \( A \) - (C) The complement of \( A \) - (D) The cardinality of \( A \) #### Explanation: - **Question 3 Analysis**: This question involves logical operators. The expression \( p \wedge \neg p \) is a conjunction of \( p \) and its negation, which results in a contradiction and is thus always false. - **Question 4 Analysis**: The notation \(\overline{A}\) typically represents the complement of set \( A \), meaning all elements not in \( A \), assuming a universal set context is given.
Expert Solution
Step 1

Note:-

p q p∧q
T T      T
T F      F
F T      F
F F      F

 

 

Part (3):- p∧¬p

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