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Consider the statements: A: Vp.Q((-p-9--9-)) 8. Vp.q((p-q-)) Which claim is true? 3- (9 ATE VTE OA is false, B is false. OA is false, B is true. OA is true, B is true. OA is true, B is false.

Consider the statements: A: Vp.Q((-p-9--9-)) 8. Vp.q((p-q-)) Which claim is true? 3- (9 ATE VTE OA is false, B is false. OA is false, B is true. OA is true, B is true. OA is true, B is false.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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**Example Question on Logical Predicates** *Suppose \( p \) and \( q \) denote arbitrary predicates.* Consider the statements: **A:** \( \forall p, q ( (\lnot p \implies q) \implies (\lnot q \implies \lnot p) ) \) **B:** \( \forall p, q ( (\lnot p \implies q) \implies (\lnot q \implies p) ) \) Which claim is true? - \( \bigcirc \) A is false, B is false. - \( \bigcirc \) A is false, B is true.
Transcribed Image Text:**Example Question on Logical Predicates** *Suppose \( p \) and \( q \) denote arbitrary predicates.* Consider the statements: **A:** \( \forall p, q ( (\lnot p \implies q) \implies (\lnot q \implies \lnot p) ) \) **B:** \( \forall p, q ( (\lnot p \implies q) \implies (\lnot q \implies p) ) \) Which claim is true? - \( \bigcirc \) A is false, B is false. - \( \bigcirc \) A is false, B is true.
### Logic Problem Analysis **Problem Statement:** Consider the statements: - **A:** ∀p ∀q (┐(p → q) → (┐q → ┐p)) - **B:** ∀p ∀q (┐(p → q) → (┐q → p)) Which claim is true? - ○ A is false, B is true. - ○ A is false, B is true. - ○ A is true, B is true. - ○ A is true, B is false. **Answer Choices:** 1. A is false, B is true. 2. A is false, B is true. 3. A is true, B is true. 4. A is true, B is false. **Graph/Diagram Explanation:** The image also contains a truth table for logical operations which includes variables and various logical connectives like AND (∧), OR (∨), and implication (→). The focus of this truth table seems to be on evaluating specific logical statements involving these operations. Each row in the table likely represents a different combination of truth values for the variables p and q and the resulting values for the logical expressions of interest. **Notes:** There is a handwritten number "6" on the right side of the image. This could denote the next question or indicate some reference value, but it does not affect the interpretation of the problem statements or the truth table directly. In an educational context, this problem could be used to teach students about logical implication and the use of truth tables to verify logical statements.
Transcribed Image Text:### Logic Problem Analysis **Problem Statement:** Consider the statements: - **A:** ∀p ∀q (┐(p → q) → (┐q → ┐p)) - **B:** ∀p ∀q (┐(p → q) → (┐q → p)) Which claim is true? - ○ A is false, B is true. - ○ A is false, B is true. - ○ A is true, B is true. - ○ A is true, B is false. **Answer Choices:** 1. A is false, B is true. 2. A is false, B is true. 3. A is true, B is true. 4. A is true, B is false. **Graph/Diagram Explanation:** The image also contains a truth table for logical operations which includes variables and various logical connectives like AND (∧), OR (∨), and implication (→). The focus of this truth table seems to be on evaluating specific logical statements involving these operations. Each row in the table likely represents a different combination of truth values for the variables p and q and the resulting values for the logical expressions of interest. **Notes:** There is a handwritten number "6" on the right side of the image. This could denote the next question or indicate some reference value, but it does not affect the interpretation of the problem statements or the truth table directly. In an educational context, this problem could be used to teach students about logical implication and the use of truth tables to verify logical statements.
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