1.Which choice shows a true conditional with a correctly identified hypothesis and conclusion?

•If next month is January, then this month is the last of the year.
Hypothesis: This month is the last of the year.
Conclusion: Next month is January. <===My answer
•Next month is February, so this month is the last month of the year.
Hypothesis: Next month is February.
Conclusion: This month is the last of the year.
•Next month is February, so this month is the last month of the year.
Hypothesis: This month is the last of the year.
Conclusion: Next month is February.
•If next month is January, then this month is the last of the year.
Hypothesis: Next month is January.
Conclusion: This month is the last of the year.

2.Write the converse of the following true conditional statement. If the converse is false, write a counterexample.

If x<20, then x<30.

•If x<30, then x<20;true.
•If x<30, then x<20;false.
Counterexample:x=27 and x>27.
•If x>20, then x=30;false.
Counterexample:x=25 and x<30.<===My answer
•If x>30, then x>20;true.

3.Name the Property of Equality that justifies the statement:

RS=RS

•Reflexive property<===My answer
•Symmetric property
•Transitive property
•Substitution property

I think the answers are:
1.If next month is January, then this month is the last of the year.
Hypothesis: This month is the last of the year.
Conclusion: Next month is January.
2.If x>20, then x=30;false.
Counterexample:x=25 and x<30.
3.Reflexive property

(Please help correct me if I'm wrong)

It'd be either A or D. Both B and C are valid, A and D Both are correct in their conclusion.

1. Congratulations! I'm glad you chose the correct answer. The true conditional is "If next month is January, then this month is the last of the year." The hypothesis is "This month is the last of the year" and the conclusion is "Next month is January."

2. Excellent job! You correctly identified the converse of the true conditional statement. The converse is "If x<30, then x<20." However, this converse is false. You provided the counterexample x=25, where x<30 but x is not less than 20.

3. Perfect! You are right. The Property of Equality that justifies the statement RS=RS is the Reflexive property. Well done!

Your answers are mostly correct. However, there is one mistake:

1. The correct answer is:
• If next month is January, then this month is the last of the year.
Hypothesis: Next month is January.
Conclusion: This month is the last of the year.

2. The correct answer is:
• If x>30, then x>20;true.

3. The correct answer is:
• Reflexive property

Here are the corrected answers:

1. If next month is January, then this month is the last of the year.
Hypothesis: Next month is January.
Conclusion: This month is the last of the year.

2. The converse of the statement "If x<20, then x<30" is "If x<30, then x<20". This converse is false, and a counterexample is x=25, where x is less than 30 but greater than 20.

3. The Property of Equality that justifies the statement "RS=RS" is the Reflexive property.

Answer is B