Question 804234
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Original implication = p &#8594; q    (if p, then q) 
Inverse = ~p &#8594; ~q               if not p, then  not q)
Converse = q &#8594; p                if q, then p
Contrapositive = ~q &#8594; ~p        if not q, then not p
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Given the implication "If you brush your hair, then your hair will be shiny"
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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 &#8594; q = "If you brush your hair, then your hair will be shiny"
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 answer the following questions
1. what is the converse of the given implication?
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q &#8594; p = "If your hair is shiny, then you have brushed your hair"
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2. what is the inverse of the given implication?
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~p &#8594; ~q = "If you do not brush your hair, then your hair will not be shiny"
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3. what is the contrapositive of the given implication?
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~q &#8594; ~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?
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Given converse = q &#8594; 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 &#8594; 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.
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Given contrapositive = ~q &#8594; ~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 &#8594; q = If we had a blizzard, then school was canceled.

Edwin</pre>