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

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.