1st test - if then, converse, inverse and contrapositive
TRANSCRIPT
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