Summative Test Q2 Direct and Indirect Proofs

Which of the following pairs of statements are equivalent?

• conditional and inverse

• conditional and converse

• converse and contrapositive

• conditional and contrapositive

Which of the following is equivalent to a converse?

• conclusion

• contrapositive

• inverse

• hypothesis

Which of the following best describes equivalent statements?

• If both statements are true.

• If both statements are false.

• If one statement is true and the other is false.

• If statements have the same corresponding truth values.

Which of the following statement is NOT true?

• Letters T and F , respectively are assigned for truth values True and False.

• Letters T and F , respectively are assigned for truth values False and True.

• The if-then statement and the corresponding contrapositive are logically equivalent.

• The converse and inverse of an if-then statement are logically equivalent.

1. Use the table below to answer the questions that follow.

Original If-then Statement: If you study, then your score will improve.

Converse (𝐼𝑓 𝑞,ℎ𝑒𝑛 𝑝): If your score does improve, then you did study.

Which of the following best describes the truth table?

• 1. The conclusions of implications 1, 2, 3, and 4 are validated as False, True, False, and 

  True respectively.

• 1. The conclusion of implications 1, 2, 3 and 4 are validated as True, False, True, and 

  False respectively.

• 1. The hypotheses of implications 1,2,3 and 4 are validated as True, True, False, and 

  False respectively.

• 1. The hypotheses of implications 1,2,3 and 4 are validated as True, False, True, and 

  False respectively.

1. Use the table below to answer the questions that follow.

Original If-then Statement: If you study, then your score will improve.

Converse (𝐼𝑓 𝑞,ℎ𝑒𝑛 𝑝): If your score does improve, then you did study.

What decision can you make to an implication of a converse if both hypothesis and 

conclusion are false?

• true

• false

• undefined

• necessarily true

1. Use the table below to answer the questions that follow.

Original If-then Statement: If you study, then your score will improve.

Converse (𝐼𝑓 𝑞,ℎ𝑒𝑛 𝑝): If your score does improve, then you did study.

What decision can you make to an implication of a converse if the hypothesis is true and 

the conclusion is false?

• true

• false

• undefined

• necessarily true

1. Use the table below to answer the questions that follow.

Original If-then Statement: If you study, then your score will improve.

Converse (𝐼𝑓𝑞,then p): If your score does improve, then you did study.

What are the truth values can be validated to a converse given an implication “Your score did not improve, that is why you study” ?

• 1. Hypothesis (p): T 

  Conclusion (q): T

• 1. Hypothesis (p): T

  Conclusion (q): F

• 1. Hypothesis (p):F   

  Conclusion (q): T

• 1. Hypothesis (p): F 

  Conclusion (q): F

1. Use the table below to answer the questions that follow.

Original If-then Statement: If you study, then your score will improve.

Converse (𝐼𝑓 𝑞,ℎ𝑒𝑛 𝑝): If your score does improve, then you did study.

What is the implication of the converse if the hypothesis is true and the conclusion is false?

• Your score improved, so you did study.

• Your score improved, but you did not study.

• Your score did not improve, that is why you study.

• Your score did not improve, because you did not study.

1. Use the table below to answer the questions that follow.

Original If-then Statement: If you study, then your score will improve.

Converse (𝐼𝑓𝑞,then p): If your score does improve, then you did study.

What is the implication of the converse if both hypothesis and conclusion are true?

• Your score improved, because you did study.

• Your score improved, but you did not study.

• Your score did not improve, that is why you study.

• Your score did not improve, because you did not study.