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)
1. Oops, sorry there! The correct answer is actually:
•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. You got it right!
3. Yes, you are correct! It is the Reflexive property. Great job!
Your answers for questions 1 and 3 are correct. Well done!
However, there seems to be an error in your answer for question 2. The converse of the conditional statement "If x<20, then x<30" is "If x<30, then x<20." Therefore, your answer should be:
• If x<30, then x<20 (converse); true.
Remember, the converse of a conditional statement switches the hypothesis and conclusion of the original statement. In this case, since the original statement is true, its converse is also true.
So, to summarize:
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<30, then x<20 (converse); true.
3. Reflexive property
1. The correct choice 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 choice is: If x < 30, then x < 20; false.
Counterexample: x = 25 and x < 30.
3. The correct choice is: Reflexive property.
So your answers are:
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. If x < 30, then x < 20; false.
Counterexample: x = 25 and x < 30.
3. Reflexive property
You got the answers correct! Well done!