Question

Which of the following arguments are invalid and which are valid? Justify your answers by first translating each sentence into propositional logic to obtain the form of the argument. Then prove that the form is valid or invalid.

4(a) The patient is stressed if they have high blood pressure

The patient is stressed

∴ The patient has high blood pressure

4(b) They studied for the test or they failed the test

They passed the class or they retook the course

∴ They studied for the class or they retook the course

4(c) If √5 is a irrational number, the 5√5 is an irrational number

√5 is a irrational number

  ∴ 5√5 is an irrational number

  

Answer 1

In case of any queries,please revert back.

Q4. ∴ means Therefore.

(a)

The patient is stressed∴ The patient has high blood pressure

This means, Patient is stressed therefore patient is having high blood pressure.

THIS IS INVALID.

Correct Will be:-

The patient has high blood pressure ∴ The patient is stressed.

(b)

They passed the class or they retook the course∴ They studied for the class or they retook the course

This means, They passed the class ∴ They studied for the class

ie. They passed the class therefore They studied for the class

THIS IS INVALID.

Correct Will be:-

They studied for the class or they retook the course ∴ They passed the class or they retook the course

(c)

√5 is a irrational number ∴ 5√5 is an irrational number

This means, √5 is a irrational number therefore, 5√5 is an irrational number

THIS IS VALID.