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

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  • 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

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