CH6-Rules of Inference

What is an argument in logic?

• A cooking recipe

• A mathematical equation

• A sequence of statements called premises followed by a statement called the conclusion

• A piece of music

Answer explanation

An argument in logic is a sequence of statements called premises followed by a statement called the conclusion.

During a school event, Ahmed and Elissa were discussing a logical rule. What is the logical rule that states 'p→q and p' Therefore q?

• Modus Tollens

• Hypothetical Syllogism

• Modus Ponens

• Disjunctive Syllogism

Answer explanation

Modus Ponens is the logical rule that states 'p→q and p implies q', where if p is true, then q must also be true.

What is the conclusion of the argument: 'If it rains, Islem will bring an umbrella. Islem did not bring an umbrella.

• Islem did not bring an umbrella

• It did not rain

• Islem brought an umbrella

• It rained

Answer explanation

The conclusion is 'It did not snow' because if it had snowed, Paul would have missed class, but since he did not miss class, it did not snow.

During a debate competition, Dhia-Eddine argued that 'p→q and ¬q Therefore ¬p'. What is the rule of inference that Dhia-Eddine is referring to?

• Hypothetical Syllogism

• Disjunctive Syllogism

• Modus Ponens

• Modus Tollens

Answer explanation

Modus Tollens is the rule of inference that states 'p→q and ¬q implies ¬p', making it the correct choice in this scenario.

During a math competition, Ahmed and Kmar were discussing a logical rule. What is the rule of inference that states 'p and q therefore p and q'?

• Conjunction

• Modus Ponens

• Hypothetical Syllogism

• Modus Tollens

Answer explanation

The correct rule of inference is Conjunction, which states 'p and q implies p'.

During a debate competition, Feriel argued that 'p or q and ¬p therefore q' is a valid rule of inference. Which rule of inference is Feriel referring to?

• Modus Ponens

• Modus Tollens

• Simplification

• Disjunctive Syllogism

Answer explanation

The correct rule of inference is Disjunctive Syllogism, which states 'p or q and ¬p implies q'.

What is the conclusion of the argument: 'If a student is named Omar, then he is a top performer. Student is named Omar.

• Omar is not a top performer

• Omar is a top performer

• Omar is an average performer

• Omar is a poor performer

Answer explanation

The conclusion of the argument is that 'You are a good student' because the premise states 'If you get A+, then you are a good student' and 'You got A+' which leads to the conclusion that you are a good student.

What is the rule of inference that states 'If Feriel is happy, then Elissa is happy, and if Elissa is happy, then Kmar is happy, therefore Feriel is happy implies Kmar is happy'?

• Hypothetical Syllogism

• Disjunctive Syllogism

• Modus Ponens

• Conjunction

Answer explanation

The correct rule of inference that states 'p implies q and q implies r implies p implies r' is Hypothetical Syllogism.