anonymous
  • anonymous
Write the converse of the conditional statement and state whether it is true or false. If a number is a whole number, then it is an integer. A. If a number is not a whole number, then it is not an integer. The converse is false. B. If a number is an integer, then it is a whole number. The converse is false. C. If a number is not an integer, then it is not a whole number. The converse is true. D. If a number is not an integer, then it is a whole number. The converse is false.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
I believe it is C

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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
thank you for coming to help me @mathstudent55
mathstudent55
  • mathstudent55
Statement: If p then q. Converse: If q then p. Statement: If hypothesis, then conclusion. Converse: If conclusion, then hypothesis. To find the converse of an "if statement", you must first identify the hypothesis and the conclusion. Then switch their positions.
anonymous
  • anonymous
then it would be C right
mathstudent55
  • mathstudent55
Choice C. has "not" added to the hypothesis and the conclusion. Do you see any "not" in the original statement?
mathstudent55
  • mathstudent55
Look in the original statement. Here it is: \(\Large \sf If ~a ~number ~is ~a ~whole ~number, ~then ~it ~is ~an ~integer.\) What is the hypothesis? What is the conclusion?
anonymous
  • anonymous
what about B then?
mathstudent55
  • mathstudent55
The hypothesis is red, and the conclusion is green. Do you agree? \(\Large \sf If ~\color{red}{a ~number ~is ~a ~whole ~number}, ~then ~\color{green}{it ~is ~an ~integer}.\)
anonymous
  • anonymous
yes
mathstudent55
  • mathstudent55
Now switch them. You may need to slightly modify the language for the sentence to make sense. \(\Large \sf If~\color{green}{it ~is ~an ~integer} , ~then ~\color{red}{a ~number ~is ~a ~whole ~number}.\) Now we slightly adjust the language: \(\Large \sf If~\color{green}{~a ~number ~is ~an ~integer} , ~then ~\color{red}{~it ~is ~a ~whole ~number}.\)
anonymous
  • anonymous
so it's sctually D
mathstudent55
  • mathstudent55
No. D again has "not" in it. You were correct before. The answer is B. You can't add "not". You can only switch the hypothesis and the conclusion.
anonymous
  • anonymous
oo ok yea i was kind of confused and thanks
mathstudent55
  • mathstudent55
You're welcome.

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