Session 3

Question 1

What is a tautology in TFL?

Answer 1

A TFL sentence that is true on every valuation

Its truth-table has a T in every row under the main connective.

Question 2

What is a contradiction in TFL?

Answer 2

A TFL sentence that is false on every valuation

Its truth-table has an F in every row under the main connective.

Question 3

What is a contingency in TFL?

Answer 3

A TFL sentence that is true on some valuations and false on others

Its truth-table has both Ts and Fs under the main connective.

Question 4

True or false: A tautology is informative.

Answer 4

FALSE

A tautology is not informative because it is true regardless of the situation.

Question 5

True or false: A contradiction is informative.

Answer 5

FALSE

A contradiction is not informative because it is false regardless of the situation.

Question 6

True or false: A contingency is informative.

Answer 6

TRUE

A contingency is informative because it can be true or false depending on the situation.

Question 7

What does it mean for sentences to be logically equivalent?

Answer 7

They are true and false under the exact same conditions

This means they have the same truth values in every valuation.

Question 8

What does it mean for sentences to be jointly consistent?

Answer 8

There is at least one valuation on which they are all true together

This indicates that the sentences can coexist without contradiction.

Question 9

What does it mean for sentences to be jointly inconsistent?

Answer 9

There is no valuation on which they are all true together

This indicates that the sentences cannot coexist without contradiction.

Question 10

An argument is valid

Answer 10

if and only if the premises entail the conclusion

This definition emphasizes the relationship between premises and conclusion in logical arguments.

Question 11

An argument is valid

Answer 11

if and only if it is not possible that the premises are all true and the conclusion is false

This definition highlights the necessity of the conclusion being true when the premises are true.

Question 12

An inference or argument of the form: A 1, A 2, …, A n ∴ B is logically valid iff

Answer 12

In each consistent valuation in which all premises A 1, A 2, …, A n are true, the conclusion B is also true

This definition provides a formal structure for assessing the validity of arguments.