Give the tautological form of modus ponens, modus inllcns, and the hypothetical syllogism, and prove that each is a valid argument,Prove that “affirming the consequent” and “denying 丨he antecedent” are invalid by giving the appropriate lines from the truth tables of their tautolr^gicai forms.Rewrite the following arguments symbolically and determine the validity of each.If John graduates he gets the job.John does not get the job.Therefore John does not graduate.If Mary wears the green hat she leads the band.Mary does not wear the green hat.Therefore Mary does not lead the band.Either Fred will sing or the cat will bark.The cat won't bark.Therefore Fred will sing.Determine the validity of each of the following arguments.Either John will run or Mary will speak.If Mary speaks, then Fred will fly and the moon is purple.The moon is not purple.Thus John will run.If the cow jumps the cat will dance.If the dog barks the cow will jump.The dog will not bark.Thus the cat will not dance.Determine the validity of each of the following.(a) P 今〜Q (b) PvRR今Q Q^RT^R Ty 〜RP______ 〜T.T TV 1. Give the tautological form of modus ponens, modus inllcns, and thehypothetical syllogism, and prove that each is a valid argument,2. Prove that "affirming the consequent" and "denying I he antecedent" areinvalid by giving the appropriate lines from the truth tables of their tautolr^gicaiforms.3. Rewrite the following arguments symbolically and determine the validity ofeach.(a) If John graduates he gets the job.John does not get the job.Therefore John does not graduate.(b) If Mary wears the green hat she leads the band.Mary does not wear the green hat.Therefore Mary does not lead the band.(c) Either Fred will sing or the cat will bark.The cat won't bark.Therefore Fred will sing. 4. Determine the validity of each of the following arguments.(a) Either John will run or Mary will speak.If Mary speaks, then Fred will fly and the moon is purple.The moon is not purple.Thus John will run.(b) If the cow jumps the cat will dance.If the dog barks the cow will jump.The dog will not bark.Thus the cat will not dance.5. Determine the validity of each of the following.(а) Р ~о(b) РуRQ^RТу RT^RP.TTV

Tautological form of Modus Ponens: p→q∧p→q Tautological form of Modus Inllcns: p→q∧~q→~p…

Answered: 1. Give the tautological form of modus…

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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Give the tautological form of modus ponens, modus inllcns, and the hypothetical syllogism, and prove that each is a valid argument,
Prove that “affirming the consequent” and “denying 丨he antecedent” are invalid by giving the appropriate lines from the truth tables of their tautolr^gicai forms.
Rewrite the following arguments symbolically and determine the validity of each.

If John graduates he gets the job.

John does not get the job.

Therefore John does not graduate.

If Mary wears the green hat she leads the band.

Mary does not wear the green hat.

Therefore Mary does not lead the band.

Either Fred will sing or the cat will bark.

The cat won't bark.

Therefore Fred will sing.

Determine the validity of each of the following arguments.

Either John will run or Mary will speak.

If Mary speaks, then Fred will fly and the moon is purple.

The moon is not purple.

Thus John will run.

If the cow jumps the cat will dance.

If the dog barks the cow will jump.

The dog will not bark.

Thus the cat will not dance.

Determine the validity of each of the following.

(a) P 今〜Q (b) PvR

R今Q Q^R

T^R Ty 〜R

P______ 〜T

.T TV

1. Give the tautological form of modus ponens, modus inllcns, and the
hypothetical syllogism, and prove that each is a valid argument,
2. Prove that "affirming the consequent" and "denying I he antecedent" are
invalid by giving the appropriate lines from the truth tables of their tautolr^gicai
forms.
3. Rewrite the following arguments symbolically and determine the validity of
each.
(a) If John graduates he gets the job.
John does not get the job.
Therefore John does not graduate.
(b) If Mary wears the green hat she leads the band.
Mary does not wear the green hat.
Therefore Mary does not lead the band.
(c) Either Fred will sing or the cat will bark.
The cat won't bark.
Therefore Fred will sing.

4. Determine the validity of each of the following arguments.
(a) Either John will run or Mary will speak.
If Mary speaks, then Fred will fly and the moon is purple.
The moon is not purple.
Thus John will run.
(b) If the cow jumps the cat will dance.
If the dog barks the cow will jump.
The dog will not bark.
Thus the cat will not dance.
5. Determine the validity of each of the following.
(а) Р ~о
(b) РуR
Q^R
Ту R
T^R
P
.T
TV

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