[ { original: $._("If it rains today, soccer practice will be canceled."), converse: $._("If soccer practice is canceled today, then it did rain."), inverse: $._("If it does not rain today, soccer practice will not be cancelled."), contrapositive: $._("If soccer practice is not canceled today, then it did not rain.") }, { original: $._("When I'm hungry, I eat pizza."), converse: $._("If I eat pizza, then I am hungry."), inverse: $._("If I am not hungry, then I do not eat pizza."), contrapositive: $._("If I do not eat pizza, then I am not hungry.") }, { original: $._("If I study really hard, I will ace the test."), converse: $._("If I aced the test, then I studied really hard."), inverse: $._("If I do not study really hard, then I will not ace the test."), contrapositive: $._("If I did not ace the test, then I did not study really hard.") }, { original: $._("John likes sushi."), converse: $._("If a person likes sushi, then the person is John."), inverse: $._("If a person is not John, then the person does not like sushi."), contrapositive: $._("If a person does not like sushi, then the person is not John.") }, { original: $._("If two angles are vertical angles, then the two angles are congruent."), converse: $._("If two angles are congruent angles, then the two angles are vertical angles."), inverse: $._("If two angles are not vertical angles, then the two angles are not congruent."), contrapositive: $._("If two angles are not congruent, then the angles cannot be vertical angles.") }, { original: $._("My dad has to take me to school when I miss the bus."), converse: $._("If my dad takes me to school, then I must have missed the bus."), inverse: $._("If I do not miss the bus, then my dad does not have to take me to school."), contrapositive: $._("If my dad does not have to take me to school, then I did not miss the bus.") }, { original: $._("All squares are four-sided polygons."), converse: $._("All four-sided polygons are squares."), inverse: $._("All polygons that are not squares do not have four sides."), contrapositive: $._("If a polygon does not have four sides, then it is not a square.") }, { original: $._("All bicycles have two wheels."), converse: $._("All vehicles with two wheels are bicycles."), inverse: $._("All vehicles that are not bicycles do not have two wheels."), contrapositive: $._("If a vehicle does not have two wheels, it is not a bicycle.") }, { original: $._("If it is Thanksgiving, then I will have a big dinner."), converse: $._("If I have a big dinner, then it is Thanksgiving."), inverse: $._("If it is not Thanksgiving, then I will not have a big dinner."), contrapositive: $._("If I did not have a big dinner, then it is not Thanksgiving.") }, { original: $._("If I go to the Yankees game, I will have a hot dog."), converse: $._("If I don't go to the Yankees game, I will not have a hot dog."), inverse: $._("If I have a hot dog, then I will go to the Yankees game."), contrapositive: $._("If I don't have a hot dog, then I did not go to the Yankees game.") }, { original: $._("Eating spinach makes you stronger."), converse: $._("If you are getting stronger, then you must be eating spinach."), inverse: $._("If you are not eating spinach, then you will not get stronger."), contrapositive: $._("If you are not getting stronger, then you are not eating spinach.") }, { original: $._("You should not use your cell phone when driving a car."), converse: $._("If you are not using your cell phone, then you are driving a car."), inverse: $._("If you are not driving a car, then you should use your cell phone."), contrapositive: $._("If you are using your cell phone, then you should not be driving a car.") }, { original: $._("If a number is divisible by 10, then it is an even number."), converse: $._("If a number is even, then it is divisible by 10."), inverse: $._("If a number is not divisible by ten, then it is not an even number."), contrapositive: $._("If a number is not even, then it is not divisible by 10.") } ]
randFromArray(PROBLEMS) $._("Yes, it can be deduced from the first statement") $._("No, it cannot be deduced from the first statement") randFromArray([ "converse", "inverse", "contrapositive" ]) PROBLEM[STATEMENT_TYPE] STATEMENT_TYPE === "contrapositive" ? MUST : MIGHT

Assume this first statement is true:

PROBLEM.original

Logically, can you deduce that this second statement must be true from the first one?

STATEMENT

ANS

- MUST
- MIGHT

Is the second statement the converse, inverse, or contrapositive of the original statement?

The second statement is the contrapositive of the original statement.

The contrapositive is logically equivalent to the original statement, so yes, the second statement can be deduced from the first statement.

The second statement is the converse of the original statement.

The converse is not logically equivalent to the original statement, so no, the second statement cannot be deduced from the first statement.

The second statement is the inverse of the original statement.

The inverse is not logically equivalent to the original statement, so no, the second statement cannot be deduced from the first statement.

randFromArray(PROBLEMS) PROBLEM.contrapositive [PROBLEM.converse, PROBLEM.inverse]

Assume this original statement below is true:

PROBLEM.original

Choose the statement that must also be true logically:

ANS

- option

Only the contrapositive of the original statement must be true.

Find the contrapositive. In other words, find the statement that reverses and negates both the hypothesis and conclusion.

In this case, the contrapositive is "PROBLEM.contrapositive"

[$._("the original statement"), $._("the converse"), $._("the inverse"), $._("the contrapositive")] randRange(0, 3) NAMES[3-CASE] shuffle((function(){var opt = NAMES.slice(); opt.splice(CASE, 1); return opt;})())

If the original statement is true, then which other statement must be true logically? If the converse is true, then which other statement must be true logically? If the inverse is true, then which other statement must be true logically? If the contrapositive is true, then which other statement must be true logically?

ANS

- option

The original conditional statement and its contrapositive are logically equivalent, and the converse and the inverse are logically equivalent.

Logically equivalent statements have the same truth-value.

Because the original statement is true, the contrapositive is also logically true.

Because the converse is true, the inverse is also logically true.

Because the inverse is true, the converse is also logically true.

Because the contrapositive is true, the original statement is also logically true.