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# 1st Test - If then, converse, inverse and contrapositive

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### Transcript

• 1. Conditionals =) Conditionals make me happy If we are doing conditionals then I am happy
• 2. 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
• 3. 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
• 4. 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
• 5. 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
• 6. The converse
• Converse just means to flip our argument around
• Start with “if p then q” then the converse is “if q then p”
• 7. 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
• 8. 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”
• 9.
• 10. 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”
• 11. 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”
• 12. 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”
• 13. The contrapositive
• The contrapositive is both the converse and the inverse at the SAME TIME
• The collision of the two!!!!111eleventy
• 14. 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”
• 15. 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”
• 16. 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”
• 17. To sum it up
• Conditional– If p then q
• Converse – if q then p
• Inverse – If !p then !q
• Contrapositive – If !q then !p
• 18. 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