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OMG HELP i hate math.


zade_o
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1. Three woman – Anna, Barbara and Jayne were arrested for the murder of Susan.  One of these three was the murderess, one was an accomplice and one was innocent.

Three statements were collected:

“Anna was not the accomplice.”

“Barbara was not the murderess.”

“Jayne is not innocent.”

The following facts are also known:

A statement does not concern the woman who gave it.
The innocent woman gave at least one statement.
Only the innocent woman tells the truth.

Which woman is the murderess?  (Explain your reasoning.)

3. Supply a conclusion, in the form of an implication, to the following argument so as to make it valid.

If Joe goes to a party, he does not fail to brush his hair.
To look fascinating it is necessary that Joe be tidy.  If Joe
is an opium eater, then he has no self-command.  If Joe
brushes his hair, he looks fascinating.  Joe wears white kid
gloves only if he goes to a party.  Having no self-command
is sufficient to make Joe look untidy.  Therefore, ….

4. Use the properties of logical equivalence to show that  ~(p<->q) = (~q)<->p
    ( what the hell? it doesn't = … I did a truth table for it? anyone know this?.....)

1.  Prove the statement below by contrapositive.

If  is a positive real number, then  .

2. Prove the statement in #1 by contradiction.

More might be coming later.......... but anyways. I gotta finish these by 7 tonight. And I'm STUCK!
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ASSUMPTION 1: Barb is innocent.

Barbara says: “Jayne is not innocent.” and tells the truth. Jayne is guilty of something.
Jayne says: “Anna was not the accomplice.” and lies, ergo Anna is the accomplice
Anna says: "Barbara was not the murderess" and lies, ergo Barb is the murderess
IMPOSSIBLE: Barb cant be innocent and the murderess

Anna says: “Jayne is not innocent.” and lies, Jayne is innocent.
Barbara says: “Anna was not the accomplice.” and tells the truth, anna is not accomplice but the murderer then.
Jayne says: "Barbara was not the murderess" and lies. Barbara is the murderess.
IMPOSSIBLE: Jayne and Barbara both cant be innocent. Babrabara cant tell the truth and be the murderess.

ERGO BARBARA IS NOT INNOCENT

rinse and repeat for the other two people.
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