anonymous
  • anonymous
determine which, if any, of the 3 statements are equivalent. I. If the boat was leaking, then mary was not seated in the boat. II. If the boat was leaking, then Mary was seated in the boat. III. If Mary was not seated in the boat, then the boat was not leaking
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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KingGeorge
  • KingGeorge
Like the last one, first we need to find what p and q are. In this case, let p="The boat was leaking." q="Mary was seated in the boat." Can you write out the statements for I, II, and III now?
anonymous
  • anonymous
I. p ---> ~q
anonymous
  • anonymous
II. p ---> q

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anonymous
  • anonymous
III. ~q --> ~p
KingGeorge
  • KingGeorge
That looks correct.
KingGeorge
  • KingGeorge
So now write out the truth tables for each one, and compare them.
anonymous
  • anonymous
I and III equivalent
KingGeorge
  • KingGeorge
What did you get for I?
anonymous
  • anonymous
FTTT
KingGeorge
  • KingGeorge
That looks correct. Check what you got for III again.
Directrix
  • Directrix
I think that i. and iii. are logically equivalent because they are contrapositives of each other. i. p --> ~q. ii. p --> q iii. ~(~q) --> ~p meaning q --> ~p
anonymous
  • anonymous
III. FTTT
anonymous
  • anonymous
F-->F = F?
KingGeorge
  • KingGeorge
Are you using (q --> ~p) or (~q --> ~p) for III? For some reason, I'm not getting FTTT for III. F -->F = T
anonymous
  • anonymous
i'm using ~q-->~p
anonymous
  • anonymous
ok.
anonymous
  • anonymous
so my III is TTTT
anonymous
  • anonymous
that's not right
anonymous
  • anonymous
TFTT?
KingGeorge
  • KingGeorge
I keep getting TFTT. Yes. That looks correct.
KingGeorge
  • KingGeorge
Is that also what you got for II?
anonymous
  • anonymous
F-->F = T?
KingGeorge
  • KingGeorge
Correct. It's a little weird, but that is true.
anonymous
  • anonymous
ok. II, III equiv
KingGeorge
  • KingGeorge
That's also what I'm getting.
anonymous
  • anonymous
cool thanks
KingGeorge
  • KingGeorge
You're welcome. I've got to go now, so good luck with the rest of your problems.
anonymous
  • anonymous
thanks so much!

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