Examination Questions And Answers English Work Sheet (Page 6 of 7) in pdf

Examination Questions And Answers English Work Sheet Page 6

Suppose one of the premises of an argument is logic equivalent to the conclusion.

What, if anything, can you conclude about the argument’s validity?

A. Answers

1. a. p, p ⊃ q, ~ p ⊃ q, ~ (p ≡ q) ⊃ r

b. p, p ∨ q, p ∨ (q ⋅ r), p ∨ (q ⋅ ~ r)

2. There would be 2

= 32 rows of the truth table.

If an argument’s premises are not consistent then it will be impossible for all of

them to be true. Therefore, the argument must be valid, because it will be

impossible for the premises to be true and the conclusion false.

Any argument with a conclusion of the form p ∨ ~ p will have a conclusion that is

a tautology, and thus a conclusion that cannot be false. Thus, it will be impossible

for that argument to have all true premises and a false conclusion, and so it will be

valid.

a. Because every sentence, tautologous, contradictory, or contingent, is a

substitution instance of some contingent sentence form or other. For instance,

every sentence is a substitution instance of the contingent sentence form p.

b. We can define a contingent sentence as a sentence that is not a substitution

instance of any tautological or contradictory sentence form.

If one of the premises of an argument is logically equivalent to the conclusion,

then the premise and the conclusion will always have the same truth value. Thus,

it will be impossible for that argument to have all true premises and a false

conclusion, and so it will be valid.

B. Tautologies, Contradictions, and Contingent Sentences

Determine by truth table analysis which of the following sentence forms are tautologous,

which are contradictory, and which are contingent:

(p ∨ q) ≡ [(p ⋅ ~ q) ∨ q]

(p ⊃ ~ q) ⊃ ~ (q ⊃ ~ p)

(p ⊃ q) ∨ (q ⊃ r)

~ [(~ p ∨ q) ≡ (~ q ⊃ ~ p)]

p ≡ (q ≡ p)

B. Answers

Tautologous

Contingent

Tautologous

Contradictory

Contingent

Examination Questions And Answers English Work Sheet Page 6