4. Let p and q be the propositions p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and fogical connectives, including negation. a. You do not drive over 65 miles per hour. b. You do not drive over 65 miles per hour, but you do not have a speeding ticket. C. Driving over 65 miles per hour is sufficient for getting a speeding ticket. 5. Show that each of these conditional statements is a tautology using truth tables. a. (p Aq)-p b. p (p V q) C. ¬p → (p → q)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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answer 4 & 5

4. Let p and q be the propositions
p: You drive over 65 miles per hour.
q: You get a speeding ticket.
Write these propositions using p and q and fogical connectives, including negation.
a. You do not drive over 65 miles per hour.
b. You do not drive over 65 miles per hour, but you do not have a speeding ticket.
C. Driving over 65 miles per hour is sufficient for getting a speeding ticket.
5. Show that each of these conditional statements is a tautology using truth tables.
a. (p Aq)p
b. p (p V q)
→ (p q)
(b + d) + d.)
Transcribed Image Text:4. Let p and q be the propositions p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and fogical connectives, including negation. a. You do not drive over 65 miles per hour. b. You do not drive over 65 miles per hour, but you do not have a speeding ticket. C. Driving over 65 miles per hour is sufficient for getting a speeding ticket. 5. Show that each of these conditional statements is a tautology using truth tables. a. (p Aq)p b. p (p V q) → (p q) (b + d) + d.)
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