Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Prove that the following propositions are tautologies using rules of inference. a)   ̴ ((p˄q) ˄  ̴ (p˅q)) b)  ̴ (p-->q) --> p

Prove that the following propositions are tautologies using rules of inference. a)   ̴ ((p˄q) ˄  ̴ (p˅q)) b)  ̴ (p-->q) --> p

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.
Chapter2: Parallel Lines
Section2.CT: Test
Problem 3CT: To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof...
See similar textbooks
icon
Related questions
Question

Prove that the following propositions are tautologies using rules of inference.

a)   ̴ ((p˄q) ˄  ̴ (p˅q))

b)  ̴ (p-->q) --> p

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

The answer provided did not use the rules of inference to prove that the propositions are tautologies which is what the original question asked. Can the answer to this problem be provided by using the rules of inference?

itions: Logic and Proofs TABLE 1 Rules of Inference. Rule of Inference P P-9 :. 9 -q P-9 קר . P-9 9-r .. pr PV q P :.qu P :: pv q p^ q .. P P 9 :. p^g pv q pvr :: qvr Tautology (p^(p-q)) → 9 (-q ^ (p →q)) ((p →q) ^ (q→r)) → (p → r) → P - ((pvq) ^-p) → 9 P→ (pv q) (p^q) → р ((p) ^ (q)) → (p^q) ((pvq) ^ (p Vr)) → (qvr) This is an argument that uses the addition rule. Name Modus ponens Modus tollens Hypothetical syllogism Disjunctive syllogism Addition Simplification Conjunction Resolution LE 4 State which rule of inference is the basis of the following argument: "It is below raining now. Therefore, it is below freezing now." Solution: Let p be the proposition "It is below freezing now," and let q be the prop raining now." This argument is of the form si botellons de l on biley sus to estu
Transcribed Image Text:itions: Logic and Proofs TABLE 1 Rules of Inference. Rule of Inference P P-9 :. 9 -q P-9 קר . P-9 9-r .. pr PV q P :.qu P :: pv q p^ q .. P P 9 :. p^g pv q pvr :: qvr Tautology (p^(p-q)) → 9 (-q ^ (p →q)) ((p →q) ^ (q→r)) → (p → r) → P - ((pvq) ^-p) → 9 P→ (pv q) (p^q) → р ((p) ^ (q)) → (p^q) ((pvq) ^ (p Vr)) → (qvr) This is an argument that uses the addition rule. Name Modus ponens Modus tollens Hypothetical syllogism Disjunctive syllogism Addition Simplification Conjunction Resolution LE 4 State which rule of inference is the basis of the following argument: "It is below raining now. Therefore, it is below freezing now." Solution: Let p be the proposition "It is below freezing now," and let q be the prop raining now." This argument is of the form si botellons de l on biley sus to estu
Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS