Modus Ponens

What is the name of the following rule of inference:

(p→q)˄p ⸫ q

• Modus ponens

• Modus tollens

• Conditionalization

• Resolution

Which Logical Pattern: If Michael buys a car, he can drive to work. Michael bought a car this week, so, therefore, he can drive to work.

• x then y, x is true, therefore y (modus ponens)

• x then y, not y, therefore not x (modus tollens)

• if x then y, if y then z, therefore if x then z (hypothetical syllogism)

• either x or y, not x, therefore y (disjunctive syllogism)

What is z in this argument (if x then y, if y then z, therefore if x then z):

If you get good grades, then it will be easier to get a good job. If you get a good job, you will be happier. Therefore if you get good grades, you will be happier.

• get good grades

• get a good job

• be happier

Consider the following premisses and conclusion. Decide in each case whether the conclusion follows from the given premisses by means of a valid rule of inference. c. If Bill signed the bill, then he caused a controversy. He signed the bill, so therefore he caused a controversy.

• Valid by modus tollens. Premisses: p → q, ~q Conclusion: ~p

• Valid by modus ponens. Premisses: p → q, p Conclusion: q

• Invalid.

Identify the rule of inference: If it rains, the ground will be wet. It is raining, so the ground is wet.

• Modus ponens

• Modus tollens

• Hypothetical syllogism

• Disjunctive syllogism

Which logical reasoning is used here: If Sarah studies, she will pass the exam. Sarah studied, therefore she passed the exam.

• Modus ponens

• Modus tollens

• Affirming the consequent

• Denying the antecedent

What is the conclusion in this argument: If the sun sets, it will be dark. The sun has set.

• It will be dark

• The sun will rise

• It will be sunny

• The moon will appear

Choose the correct inference: If the alarm rings, there is a fire. The alarm is ringing.

• There is a fire

• There is no fire

• The alarm is broken

• The fire is out

Determine the logical pattern: If the book is interesting, I will read it. The book is interesting.

• I will read it

• I will not read it

• I will buy it

• I will sell it

What is the correct conclusion: If the team wins, they will celebrate. The team won.

• They will celebrate

• They will not celebrate

• They will practice

• They will rest