4. Construct truth tables for the compound propositions: a) (p→ q) V – (p → q) b) (p V - q) A (q V -p) с) (р^-9) —R d) (р — q) л(р — R) 5. Show that (¬ p V q) → ((p ^ ¬q) is a tautology. 6. Use the laws of propositional logic to show that: a) (p V q) ^ ¬q="p^q b) (-pV q) → (p A q) = P c) pA (-p→ q) = P (Note not use Truth Table) 7. Test the validity of the following arguments by constructing truth tables: a) If it rains, Joe will be sick Joe was not sick : It did not rain b) Either you study or you play You do not study (exclusiv : You play 8. Prove that the sum of an even umber and an odd number is odd. 9. Suppose X is an integer. Prove that if 2X+3 is odd, then X is odd. 10. Suppose n us an integer. Prove that if n +5 is number odd, then n is even 11. Prove that the of product of 2 even integer is even. 12. Prove that V3 is irrational.
4. Construct truth tables for the compound propositions: a) (p→ q) V – (p → q) b) (p V - q) A (q V -p) с) (р^-9) —R d) (р — q) л(р — R) 5. Show that (¬ p V q) → ((p ^ ¬q) is a tautology. 6. Use the laws of propositional logic to show that: a) (p V q) ^ ¬q="p^q b) (-pV q) → (p A q) = P c) pA (-p→ q) = P (Note not use Truth Table) 7. Test the validity of the following arguments by constructing truth tables: a) If it rains, Joe will be sick Joe was not sick : It did not rain b) Either you study or you play You do not study (exclusiv : You play 8. Prove that the sum of an even umber and an odd number is odd. 9. Suppose X is an integer. Prove that if 2X+3 is odd, then X is odd. 10. Suppose n us an integer. Prove that if n +5 is number odd, then n is even 11. Prove that the of product of 2 even integer is even. 12. Prove that V3 is irrational.
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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Transcribed Image Text:4. Construct truth tables for the compound propositions:
а) (р — q) v - (ред)
b) (p V – q) ^ (q V -p)
с) (р^-9) —R
d) (р — q) л(р — R)
5. Show that (-pV q) → ((p ^¬q) is a tautology.
6. Use the laws of propositional logic to show that:
a) (p V q) ^ ¬q="p ^ q
b) (-pVq) — (рлq) %3DР
c) pA(-p → q) = P
(Note not use Truth Table)
7. Test the validity of the following arguments by constructing truth tables:
a) If it rains, Joe will be sick
Joe was not sick
: It did not rain
b) Either you study or you play
You do not study
: You play
(exclusive OR)
8. Prove that the sum of an even number and an odd number is odd.
9. Suppose X is an integer. Prove that if 2X+3 is odd, then X is odd.
10. Supposen us an integer. Prove that if n3
+5 is number odd, then n is even
11. Prove that the of product of 2 even integer is even.
12. Prove that v3 is irrational.
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