Week 6

Question 1

Which of the following best defines validity in logic? -

Answer 1

A conclusion is valid if it logically follows from the premises regardless of whether the premises are true.

Question 2

José is Spanish; most Spanish people are Catholics; so José is Catholic.-

Answer 2

Inductively Valid

Question 3

What makes an inference deductively valid? -

Answer 3

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

Question 4

In logic what does the symbol P→Q represent? -

Answer 4

If P is true, then Q must be true.

Question 5

Which of the following statements is an example of a universal quantifier? -

Answer 5

Every student passed the exam.

Question 6

What is the significance of truth functions in logic? -

Answer 6

They determine the truth value of a proposition based on its components.

Question 7

In the context of logical quantifiers what does the statement “Someone is happy” imply? -

Answer 7

There is at least one person who is happy.

Question 8

Which of the following is an example of inductive validity? -

Answer 8

“All the swans I’ve seen are white so all swans must be white.”

Question 9

What does the existential quantifier ∃ indicate in formal logic? -

Answer 9

It asserts that there is at least one object in a domain that satisfies a condition.

Question 10

Symbolize the following inference, and evaluate its validity:

Everyone wanted to win the prize; so the person who won the race wanted to win the prize.

Let:
xP be ‘x wanted to win the prize’.
xR be ‘x won the race’.

And let the objects in question be people. Then the inference is:

Answer 10

Invalid