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Fill in the blanks in the following truth table. -ppvr (pvr) →q ? v Pqr TTT ? TFT ? ♥ FTT ? ♥ FFT ? TITF ? TFF ? FTF ? ♥ FFF ? > ? ? ? ? ? ? ?

Fill in the blanks in the following truth table. -ppvr (pvr) →q ? v Pqr TTT ? TFT ? ♥ FTT ? ♥ FFT ? TITF ? TFF ? FTF ? ♥ FFF ? > ? ? ? ? ? ? ?

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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### Question 11 **Objective:** Fill in the blanks in the following truth table. **Instructions:** Use the given initial truth values to complete the columns for the logical expressions ~p, p ∨ r, and (~p ∨ r) → q. | p | q | r | ~p | p ∨ r | (~p ∨ r) → q | |---|---|---|----|-------|--------------| | T | T | T | | | | | T | F | T | | | | | T | T | F | | | | | T | F | F | | | | | F | T | T | | | | | F | T | F | | | | | F | F | T | | | | | F | F | F | | | | **Explanation:** - **Column p, q, r:** Initial truth values for variables. - **Column ~p:** Logical negation of p. If p is TRUE (T), ~p is FALSE (F). If p is FALSE (F), ~p is TRUE (T). - **Column (p ∨ r):** Logical disjunction (OR) between p and r. The result is TRUE if at least one of p or r is TRUE. - **Column (~p ∨ r) → q:** Logical implication. The expression (~p ∨ r) is TRUE if either ~p or r is TRUE. The implication (~p ∨ r) → q is TRUE except when ~p ∨ r is TRUE and q is FALSE. ### Answer key: | p | q | r | ~p | p ∨ r | (~p ∨ r) → q | |------|------|------|----|--------|--------------| | TRUE | TRUE | TRUE | F | TRUE | TRUE | | TRUE | FALSE| TRUE | F | TRUE | FALSE | | TRUE | TRUE | FALSE| F | TRUE | TRUE | | TRUE | FALSE| FALSE| F | FALSE | TRUE | | FALSE| TRUE | TRUE | T | TRUE | TRUE | | FALSE| TRUE | FALSE| T | FALSE | TRUE | | FALSE| FALSE| TRUE | T
Transcribed Image Text:### Question 11 **Objective:** Fill in the blanks in the following truth table. **Instructions:** Use the given initial truth values to complete the columns for the logical expressions ~p, p ∨ r, and (~p ∨ r) → q. | p | q | r | ~p | p ∨ r | (~p ∨ r) → q | |---|---|---|----|-------|--------------| | T | T | T | | | | | T | F | T | | | | | T | T | F | | | | | T | F | F | | | | | F | T | T | | | | | F | T | F | | | | | F | F | T | | | | | F | F | F | | | | **Explanation:** - **Column p, q, r:** Initial truth values for variables. - **Column ~p:** Logical negation of p. If p is TRUE (T), ~p is FALSE (F). If p is FALSE (F), ~p is TRUE (T). - **Column (p ∨ r):** Logical disjunction (OR) between p and r. The result is TRUE if at least one of p or r is TRUE. - **Column (~p ∨ r) → q:** Logical implication. The expression (~p ∨ r) is TRUE if either ~p or r is TRUE. The implication (~p ∨ r) → q is TRUE except when ~p ∨ r is TRUE and q is FALSE. ### Answer key: | p | q | r | ~p | p ∨ r | (~p ∨ r) → q | |------|------|------|----|--------|--------------| | TRUE | TRUE | TRUE | F | TRUE | TRUE | | TRUE | FALSE| TRUE | F | TRUE | FALSE | | TRUE | TRUE | FALSE| F | TRUE | TRUE | | TRUE | FALSE| FALSE| F | FALSE | TRUE | | FALSE| TRUE | TRUE | T | TRUE | TRUE | | FALSE| TRUE | FALSE| T | FALSE | TRUE | | FALSE| FALSE| TRUE | T
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