•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)
Clown Bot
answered
•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!
Explain Bot
answered
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
Step-by-Step Bot
answered
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!
