Rules of Inference

Consider the following propositions: A: Paul is not happy with his work. B: Paul should quit his work. C: Paul needs to support his family. Determine the symbolic form of the statement: Paul is not happy with his work but if he needs to provide for his family then he should not quit his work.

• (B→A)→C

• A∧(C→¬B)

• C→(B∧A)

• A∨(C→B)

Which of the following is a valid argument?

• If gas prices go up, then prices of commodities go up. Prices of commodities go up. Therefore, gas prices went up.

• If gas prices go up, then prices of commodities go up. Prices of commodities go up. Therefore, gas prices did not go up.

• If gas prices go up, then prices of commodities go up. Gas prices went up. Therefore, prices of commodities went up.

• If gas prices go up, then prices of commodities go up. Gas prices did not go up. Therefore, prices of commodities did not go up.

Consider the following premises: Mary will study or she will hang out with her friends. She did not study. What is a valid conclusion for this argument?

• Mary did not hang out with her friends.

• Mary studied.

• Mary did not study.

• Mary hanged out with her friends.

Which of the following is a valid argument?

• If I don’t feel well, then I will stay at home. I didn’t stay at home. Therefore, I feel well.

• If I don’t feel well, then I will stay at home. I stayed at home. Therefore, I don’t feel well.

• If I don’t feel well, then I will stay at home. I feel well. Therefore, I didn’t stay at home.

• If I don’t feel well, then I will stay at home. I don’t feel well. Therefore, I did not stay at home.

Which of the following arguments is VALID?

• Burgers are expensive and the soup is hot. Therefore, burgers are expensive if and only if the soup is hot.

• Burgers are expensive and the soup is hot. Therefore, burgers are not expensive.

• Burgers are expensive and the soup is hot. Therefore, the soup is not hot.

• Burgers are expensive and the soup is hot. Therefore, burgers are expensive.

What rule of inference was used in the following argument? Premise 1: (S∨T)∨P Premise 2: ¬(S∨T)∨(Q→P) Conclusion: P∨(Q→P)

• Modus Tollens

• Resolution

• Simplification

• Hypothetical Syllogism

What rule of inference was used in the following argument? Premise 1: If tuition fee is increasing every year then many students cannot afford to pay their tuition. Premise 2: If many students cannot afford to pay their tuition, student enrollment will decline. Conclusion: If tuition fee is increasing every year, then student enrollment will decline.

• Addition

• Resolution

• Hypothetical Syllogism

• Conjunction

What rule of inference was used in the following argument? Ed’s wallet is in his back pocket. Ed is going home. Therefore, Ed’s wallet is in his back pocket and he is going home.

• Resolution

• Conjunction

• Modus Ponens

• Disjunctive Syllogism

What rule of inference was used in the following argument? Premise: Daniel will do part-time work this summer. Conclusion: Daniel will do part-time work this summer or he will go to the beach.

• Conjuction

• Addition

• Modus Tollens

• Hypothetical Syllogism