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1. (a) Show that [(pq) Ag] →p is not a tautology. (b) Make up an example (i.e., particular English statements for p and q) to illustrate how the propo- sition in part (a) can be false. (c) Insert two ("not") symbols to make the proposition in part (a) into a tautology. 2. (a) Negate the proposition Vp [(3t [R(p, t)]) VQ(p)]. Move the negation as far inside the parentheses as possible. Show all steps. Pay close attention to the parentheses. (b) Let P National park in the US t Hiking trail that doesn't allow dogs park p has trail t R(p, t) Q(p) park p is closed. Write the original proposition and its negation in English.

1. (a) Show that [(pq) Ag] →p is not a tautology. (b) Make up an example (i.e., particular English statements for p and q) to illustrate how the propo- sition in part (a) can be false. (c) Insert two ("not") symbols to make the proposition in part (a) into a tautology. 2. (a) Negate the proposition Vp [(3t [R(p, t)]) VQ(p)]. Move the negation as far inside the parentheses as possible. Show all steps. Pay close attention to the parentheses. (b) Let P National park in the US t Hiking trail that doesn't allow dogs park p has trail t R(p, t) Q(p) park p is closed. Write the original proposition and its negation in English.

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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Plz answer question 1 only in 20 mints plz it's very urgent plzzzzz
1. (a) Show that [(p→g) Aq] →p is not a tautology. (b) Make up an example (i.e., particular English statements for p and q) to illustrate how the propo- sition in part (a) can be false. (c) Insert two ("not") symbols to make the proposition in part (a) into a tautology. 2. (a) Negate the proposition Vp [(3t [R(p, t)]) VQ(p)]. Move the negation as far inside the parentheses as possible. Show all steps. Pay close attention to the parentheses. (b) Let P t R(p, t) Q(p) National park in the US Hiking trail that doesn't allow dogs park p has trail t park p is closed. Write the original proposition and its negation in English. h Gall Ah dat
Transcribed Image Text:1. (a) Show that [(p→g) Aq] →p is not a tautology. (b) Make up an example (i.e., particular English statements for p and q) to illustrate how the propo- sition in part (a) can be false. (c) Insert two ("not") symbols to make the proposition in part (a) into a tautology. 2. (a) Negate the proposition Vp [(3t [R(p, t)]) VQ(p)]. Move the negation as far inside the parentheses as possible. Show all steps. Pay close attention to the parentheses. (b) Let P t R(p, t) Q(p) National park in the US Hiking trail that doesn't allow dogs park p has trail t park p is closed. Write the original proposition and its negation in English. h Gall Ah dat
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