Which of the following is NOT logically equivalent to the statement below: Consi

Question

Which of the following is NOT logically equivalent to the statement below: Consider the following argument: If mica teaches logic, then Justin takes a nap. As we all know, Justin is lazy and is taking a nap. So, obviously, mica is teaching logic. Which of the following statements are true? The sentence, "mica is teaching logic." is a premise. The phrase, "As we all know" indicates that an inference is being made. The sentence, "Justin is lazy and is taking a nap." is a premise. Turn the following argument into a material conditional (for truth table proof). If it rains, the driving will be bad. If it snows, the driving will be bad. It will rain or it will snow. Hence, the driving will be bad. Use the following sentence letters for atomic sentences: R, D, S

Explanation / Answer

33) For any two statements P and Q , it is true that PQ ¬ P V Q

So That PQ is not equivalent to (PVQ)(¬ P V Q)

34) The sentence " Justine is lazy and is taking a nap " is premise.

35)   Let us denote

R : It is raining

D : The driving will be bad

S : It is snow

The the given argument can be written in symbolic form as follows :

R D

S D

R V S

--------------

Therefore , D

Proof :

(1)    R V S      premise

(2) ¬ R S          (2) , R V S    ¬ R S    

(3) S D                           premise

(4) ¬ R D    (2) ,(3) , use chain rule

(5) R D premise

(6) D (4),(5)

Hence D is logically follows from the given premises and the given argument is valid

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