2.1 If-Then

Statements

WARM UP

• If you are a broop, then you are a breeb.

• If you are a brelp, then you are not a brip.

• If you are not a brelp, then you are not a breeb.

• You are a breeb.Which of the following statements also must be true?

1) You are a brip.

2) You are a broop.

3) Both 4 and 5.

4) You are a brelp.

5) You are not a brip.

6) Both 1 and 2.

If-Then Statements

• If-Then Statements are also called CONDITIONALS.

• Example:

– If you smell nice, then you will meet a pretty girl.

–The hypothesis is the “If” part–The conclusion is the “then” part

If p, then q

Converse

If q, then p.If you smell nice,

then you will meet a pretty girl.• What is the converse?

• If you met a pretty girl, then you smelled nice.

Inverse

If not p, then not q.If you smell nice,

then you will meet a pretty girl.

What is the inverse of this statement?

• If you do not smell nice, then you will not meet a pretty girl.

Contrapositive

If not q, then not p. If you smell nice, then you will meet a pretty girl.

What is the contrapositive of this statement?• If you did not meet a pretty girl, then

you did not smell nice.

Four types

• The four types of ways a theorem can be written are – Conditional If p, then q.– Converse If q, then p.– Inverse If not p, then not q.– Contrapositive If not q, then not p.

• If all FOUR are TRUE, then you can write

a BICONDITIONAL.

Biconditional

• uses the words “if and only if”

p if and only if q• If segments are congruent, then their

lengths are equal.

• Segments are congruent if and only if their lengths are equal.

SAT Practice Question

• The statement “If Jill misses the bus, she will be late” is true. Which other statement must be true?

(A) If Jill does not miss the bus, she will not be late.

(B) If Jill is not late, she missed the bus.

(C) If a student misses the bus, he or she will be late.

(D) Jill is late because she missed the bus.

(E) If Jill is not late, she did not miss the bus.

SAT TRICK #1

• If the conditional is true,

• The CONTRAPOSITIVE IS TOO!

Counterexamples

• Find a counterexample for the following.

• If a line lies in a vertical plane, then the line

is vertical.

• If a number is divisible by 4 then it is

divisible by 6.

Horizontal line

16 40

Your turn!

•Come up with your own conditional.

•MOVIE TIME!!!• At 3 min