Original implication = p → q (if p, then q)
Inverse = ~p → ~q if not p, then not q)
Converse = q → p if q, then p
Contrapositive = ~q → ~p if not q, then not p
Given the implication "If you brush your hair, then your hair will be shiny"
Let p = "You brush your hair".
Let q = "Your hair is shiny".
Notice the change in the tense of the verb in q from "will be" to "is".
This is allowed to keep the statements from sounding funny, and as they might
be spoken in reality.
p → q = "If you brush your hair, then your hair will be shiny"
answer the following questions
1. what is the converse of the given implication?
q → p = "If your hair is shiny, then you have brushed your hair"
2. what is the inverse of the given implication?
~p → ~q = "If you do not brush your hair, then your hair will not be shiny"
3. what is the contrapositive of the given implication?
~q → ~p = "If your hair is not shiny, then you have not brushed your hair"
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4. If given the converse statement " If you are broke , then you spent a lot of money" what was the original implication?
Given converse = q → p = "If you are broke , then you spent a lot of money"
q = "You are broke"
p = "You spent a lot of money"
Original implication = p → q = "If you spent a lot of money, then you are broke."
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5. If given the contra positive statement, " If school is not cancelled then we did not have a blizzard", what was the original implication.
Given contrapositive = ~q → ~p = "If school is not cancelled then we did not have a blizzard
q = School is canceled
p = We had a blizzard
Original implication = p → q = If we had a blizzard, then school was canceled.
Edwin