2.1 Conditionals

2.1 Conditionals

Geometry CP

Let's Review Hypothesis & Conclusion

• Hypothesis: the part that follows IF

• Conclusion: the part that follows the THEN

Example:

• If it is Friday, then the recycling is picked up.

• Hypothesis: it is Friday

• Conclusion: the recycling is picked up.

Multiple Choice

If a number is divisible by 2, then the number is even.

What is the conclusion?

• a number is divisible by 2

• the number is even

Multiple Choice

If a number is divisible by 2, then the number is even.

What is the hypothesis?

• a number is divisible by 2

• the number is even

Fill in the Blanks

What is the hypothesis of the following statement? Type your answer carefully! No capital letters or punctuation!

If the tree has a shadow, then it is sunny outside.

Fill in the Blanks

What is the conclusion of the following statement? Type your answer carefully! No capital letters or punctuation!

If my tooth hurts, then it may have a cavity.

Let's Review Counterexamples...

• A conditional may or may not be true.

• To show FALSE, find a counterexample.

If an animal has stripes, then it is a tiger.

• THINK: it "must be" a tiger

• FALSE

• Counterexample: Zebra, Clown Fish

If it is a whale, then it is a mammal.

• THINK: it "has to be" a mammal

• TRUE

• 
  

Multiple Choice

Decide if the statement is true or false.

If the country is in Europe, then it is France.

• True

• False

Multiple Choice

Decide if the statement is true or false.

If you are in Hawaii, then you are on an island.

• True

• False

Multiple Choice

Decide if the statement is true or false.

If the plant has leaves, then it is a tree.

• True

• False

Let's review altering conditionals...

• Converse - SWITCH hyp. & conc.

• Inverse - NEGATE hyp. & conc.

• Contrapositive - SWITCH & NEGATE hyp. & conc.

Conditional: If the animal barks, then it is a seal.

• Converse: If it is a seal, then the animal barks.

• Inverse: If the animal does not bark, then it is not a seal.

• Contrapositive: If it is not a seal, then the animal does not bark.

Multiple Choice

Choose the CONVERSE of the statement:

If the animal is a cat, then it meows.

• If the animal is not a cat, then it does not meow.

• If it does not meow, then the animal is not a cat

• If it meows, then the animal is a cat.

• The animal is a cat iff it meows.

Multiple Choice

Choose the INVERSE of the statement:

If the animal is a cat, then it meows.

• If the animal is not a cat, then it does not meow.

• If it does not meow, then the animal is not a cat

• If it meows, then the animal is a cat.

• The animal is a cat iff it meows.

Multiple Choice

Choose the CONTRAPOSITIVE of the statement:

If the animal is a cat, then it meows.

• If the animal is not a cat, then it does not meow.

• If it does not meow, then the animal is not a cat

• If it meows, then the animal is a cat.

• The animal is a cat iff it meows.

Fill in the Blanks

WRITE the CONVERSE of the statement:

If it is cloudy, then it will rain.

Fill in the Blanks

WRITE the INVERSE of the statement:

If it is cloudy, then it will rain.

Fill in the Blanks

WRITE the CONTRAPOSITIVE of the statement:

If it is cloudy, then it will rain.

Fill in the Blanks

WRITE the CONVERSE of the statement:

If a figure is a rectangle, then it has exactly 4 sides.

Fill in the Blanks

WRITE the INVERSE of the statement:

If a figure is a rectangle, then it has exactly 4 sides.

Fill in the Blanks

WRITE the CONTRAPOSITIVE of the statement:

If a figure is a rectangle, then it has exactly 4 sides.