Avoiding Fallacious Reasoning: Lesson 7

The following is from Hurely 6.4 and 6.3

The corresponding conditional is when you take the premises and conjoin them with the conjunction operator, making them into one big antecedent; then, take the conclusion as the consequent.

The premises are separated by forward slash makrs. The conclusion is separated by two slash marks.

Give the corresponding conditional for the following arguments:

O ɔ ~T / ~T ɔ B // O ɔ B

((O ɔ ~T) • (~T ɔ B)) ɔ (O ɔ B)

1 translation: J ɔ E/~J//~E

2 translation: What is another way to say tautologous statement?

3 translation: What is another way to say self-contradictory statement?

4 translation: If the truth values vary depending on the truth values of the components, then what kind of classification is the statement?

5 translation: If the statement is tautologous, then the truth values under the main operator are what?

6 translation: If the statement is self-contradictory, then the truth values under the main operator are what?

7 translation: If the statement is contingent, then the truth values under the main operator are what?

8 translation: When comparing statements, the relation between them is ____________ if the truth values under the main operators are the same on each line

9 translation: When comparing statements, the relation between them is __________ if the truth values under the main operators are opposite on each line

10 translation: When comparing statements, the relation between them is ___________ if the truth values under the main operators have at least one line when the truth values are all true

11 translation: When comparing statements, the relation between them is __________ if the truth values under the main operators don’t have any line in which the truth values are all true

12 translation: For any two propositions that are logically equivalent, the biconditional statement formed by joining them with a triple bar is ___________

13 translation: Of the 4 relations, which of them are the strongest?

Answers to Lesson 7

1 answer: ((J ɔ E) • ~J) ɔ ~E
2 answer: logically true
3 answer: logically false
4 answer: contingent
5 answer: all true
6 answer: all false
7 answer: at least one true and at least one false
8 answer: logically equivalent
9 answer: contradictory
10 answer: consistent
11 answer: inconsistent
12 answer: tautologous
13 answer: logically equivalent, contradictory