Rules of inference

An argument is valid if and only if:

• The premises are true and the conclusion is true.
• The premises are true.
• The conclusion must be true if the premises are true.
• The conclusion is true.

Tags

CCSS.HSA.REI.A.1

Is this argument valid or invalid: If Ahmed goes to Paris, he will have a lot of fun. He didn't have a lot of fun. Therefore, he must not have gone to Paris.

• valid

• invalid

Is this argument valid or invalid: If a baby sleeps 10 hours, then he will learn to read. If he learns to read, he will become a CEO. Therefore, if a baby sleeps 10 hours, he will become a CEO.

• valid

• invalid

P1. If it is raining, then the streets are wet.
P2. The streets are wet.
C. Therefore, it is raining.

• Valid
• Invalid
• Sound

If you repent, you will go to heaven.
You have repented.
So you will go to heaven.

• Modus Ponens
• Modus Tollens
• Disjunctive Syllogism
• Hypothetical Syllogism 

The soul is immortal or it is mortal. The soul is not immortal. Therefore it is mortal.

• Modus Ponens

• Modus Tollens

• Hypothetical Syllogism

• Disjunctive Syllogism

Name this argument form: If P then Q. P. Therefore Q.

• modus ponens

• modus tollens

• disjunctive syllogism

• hypothetical syllogism

Tags

CCSS.HSA.REI.A.1

Determine the rules of inference for:

He studies very hard

therefore, he studies very hard Or he is a very bad student

• Modus Ponens

• Modus Tollens

• Addition

• Disjunctive Syllogism

Determine the rules of inference for:

The ice cream is vanilla flavored or chocolate flavored

The ice cream is not vanilla flavored

Therefore The ice cream is chocolate flavored

• Modus Ponens

• Modus Tollens

• Disjunctive Syllogism

• Hypothetical Syllogism

Determine the rules of inference :

If it rains, I shall not go to school

If I don't go to school, I won't need to do homework

If it rains, I won't need to do homework

• Modus Ponens

• Modus Tollens

• Disjunctive Syllogism

• Hypothetical Syllogism