randFromArray(["converse", "inverse", "contrapositive"])
{ "converse" : $._("If soccer practice will be canceled today, then it will rain."), "inverse" : $._("If it does not rain today, soccer practice will not be canceled."), "contrapositive" : $._("If soccer practice is not canceled today, then it is not raining."), "other1" : $._("If I don't like soccer, then I won't go to soccer practice."), "other2" : $._("When it rains I don't want to go to soccer practice.") } $._("it rains today") $._("it does not rain today") $._("soccer practice will be canceled") $._("soccer practice will not be canceled")

Identify the converse of the given conditional statement. Identify the inverse of the given conditional statement. Identify the contrapositive of the given conditional statement.

"If it rains today, soccer practice will be canceled."

CHOICES[TYPE]

  • value
{ "converse" : $._("If I need to wear a hat today, then the sun is bright outside."), "inverse" : $._("The sun is not bright outside, so I do not need to wear a hat."), "contrapositive" : $._("If I am not wearing a hat today, then the sun is not bright outside."), "other1" : $._("I only wear hats when it rains."), "other2" : $._("If I do not wear a hat today, then I could get sunburned.") } $._("the sun is bright outside today") $._("the sun is not bright outside today") $._("I will wear a hat") $._("I will not wear a hat")

"The sun is bright outside today, so I will wear a hat."

{ "converse" : $._("If I eat apple pie, then we will have dessert tonight."), "inverse" : $._("If we do not have dessert tonight, then I will not eat apple pie."), "contrapositive" : $._("If I did not eat apple pie, then we did not have dessert tonight."), "other1" : $._("If we do not have dessert tonight, I will be upset."), "other2" : $._("I do not like apple pie, so I will not eat dessert tonight.") } $._("we have dessert tonight") $._("we do not have dessert tonight") $._("I will eat apple pie") $._("I will not eat apple pie")

"If we have dessert tonight, I will eat apple pie."

{ "converse" : $._("All pairs of congruent angles are vertical angles."), "inverse" : $._("All pairs of angles that are not vertical angles are not congruent angles."), "contrapositive" : $._("All pairs of angles that are not congruent are not vertical angles."), "other1" : $._("Vertical angles are always congruent."), "other2" : $._("Congruent angles can be vertical angles but they don't have to be.") } $._("a pair of angles are vertical angles") $._("a pair of angles are not vertical angles") $._("the two angles are congruent") $._("the two angles are not congruent")

"All pairs of vertical angles are congruent angles."

{ "converse" : $._("If an animal eats peanuts, then it is an elephant."), "inverse" : $._("If an animal is not an elephant, then it does not eat peanuts."), "contrapositive" : $._("If an animal does not eat peanuts, then it is not an elephant."), "other1" : $._("Elephants also eat hay."), "other2" : $._("Animals that eat peanuts may also like peanut butter.") } $._("an animal is an elephant") $._("an animal is not an elephant") $._("the animal eats peanuts") $._("the animal does not eat peanuts")

"Elephants eat peanuts."

"If 3x+1=7, then x=2."

If x=2, then 3x+1=7. If 3x+1\not=7, then x\not=2. If x\not=2, then 3x+1\not=7.

  • If x=2, then 3x+1=7.
  • If 3x+1\not=7, then x\not=2.
  • If x\not=2, then 3x+1\not=7.
  • If x=4, then 3x+1=13.
  • If 3x+1=10, then x=3.

In this statement, the hypothesis is 3x+1=7 and the conclusion is x=2

Thus, when we take the converse, the hypothesis becomes x=2 and the conclusion becomes 3x+1=7.

Thus, when we take the inverse, the hypothesis becomes 3x+1\not=7 and the conclusion becomes x\not=2.

Thus, when we take the contrapositive, the hypothesis becomes x\not=2 and the conclusion becomes 3x+1\not=7.

Bringing the hypothesis and conclusion together, we find the converse of the original statement to be, "If x=2, then 3x+1=7." Bringing the hypothesis and conclusion together, we find the inverse of the original statement to be, "If 3x+1\not=7, then x\not=2." Bringing the hypothesis and conclusion together, we find the contrapositive of the original statement to be, "If x\not=2, then 3x+1\not=7."

In this statement, the hypothesis is "HYPOTHESIS" and the conclusion is "CONCLUSION"

Thus, when we take the converse, the hypothesis becomes "CONCLUSION" and the conclusion becomes "HYPOTHESIS".

Thus, when we take the inverse, the hypothesis becomes "NEG_HYPOTHESIS" and the conclusion becomes "NEG_CONCLUSION".

Thus, when we take the contrapositive, the hypothesis becomes "NEG_CONCLUSION" and the conclusion becomes "NEG_HYPOTHESIS".

Bringing the hypothesis and conclusion together, we find the converse of the original statement to be, "CHOICES[TYPE]"

Bringing the hypothesis and conclusion together, we find the inverse of the original statement to be, "CHOICES[TYPE]"

Bringing the hypothesis and conclusion together, we find the contrapositive of the original statement to be, "CHOICES[TYPE]"