Conditionals =)

Conditionals make me happy

If we are doing conditionals then I am happy

Converting from…statement to conditional

• A conditional is just another way to write a statement using the words “if” and “then”

• Our statement will be something like “if p then q”

• It is

An example

• Math teachers love their jobs• Let p = “Teaching Math”• Let q = “loving your job”• We are using the form

if p then q• So….• …..• …. =)• If you teach math then you love your job

Another example

• Students hate homework• Let p = “Being a student”• Let q = “hating homework”• We are using the form if p then q• If you are a student then you hate homework

One More Example

• Ben’s roommate plays guitar• Let p = “being Ben’s roommate”• Let q = “playing guitar”• We are using the form if p then q• If you share rent with Ben then you play guitar

The converse

• Converse just means to flip our argument around

• Start with “if p then q” then the converse is “if q then p”

Converse example

• If you teach math then you love your job• So p is “teaching math”• And q is “loving your job”• Since the converse is “if q then p” this specific

converse is ….• ……• ……. =)• If you love your job then you teach math

Another converse example

• If you share rent with Ben then you play guitar• so p is “being Ben’s roommate”• And q is “playing guitar”• The converse of the above statement would

be “If you play guitar then you share rent with Ben”

The inverse

• The inverse means to take the NOT of both statements

• If we start with “If p then q” then the inverse is “if !p then !q”

• The above reads as “If not p then not q”

Inverse example

• If you are a student then you hate homework• So p is “being a student”• And q is “hating homework”• The inverse would be “if !p then !q” so it

would be• “If you are not a student then you love

homework”

Another inverse example

• If you teach math then you love your job• So p is “teaching math”• And q is “loving your job”• The inverse would be “if !p then !q” so it

would be• “If you do not teach math then you hate your

job”

The contrapositive

• The contrapositive is both the converse and the inverse at the SAME TIME

• The collision of the two!!!!111eleventy

The contrapositive

• Our starting statement is “if p then q”• To find the contrapositive we find the

converse “if q then p”• Then we find the inverse of the converse

“if !q then !p”

Contrapositive example

• If you are a student then you hate homework• So p is “being a student”• And q is “hating homework”• The converse would be “If you hate

homework then you are a student”• Then we would take the inverse of that and

get “if you love homework then you are not a student”

Another contrapositive example

• If you teach math then you love your job• So p is “teaching math”• And q is “loving your job”• The contrapositive would be “if !q then !p”• So we have “if you hate your job then you do

not teach math”

To sum it up

• Conditional– If p then q• Converse – if q then p• Inverse – If !p then !q• Contrapositive – If !q then !p

Summing it up using geometry

• Statement: A triangle is a polygon• Conditional: If it is a triangle then it is a

polygon• converse: if it is a polygon then it is a triangle• inverse: if it is not a triangle then it is not a

polygon• contrapositive: if it is not a polygon then it is

not a triangle