Question

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

Answer 1

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?

Answer 2

I. p ---> ~q

Answer 3

II. p ---> q

Answer 4

III. ~q --> ~p

Answer 5

That looks correct.

Answer 6

So now write out the truth tables for each one, and compare them.

Answer 7

I and III equivalent

Answer 8

What did you get for I?

Answer 9

FTTT

Answer 10

That looks correct. Check what you got for III again.

Answer 11

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

Answer 12

III. FTTT

Answer 13

F-->F = F?

Answer 14

Are you using (q --> ~p) or (~q --> ~p) for III? For some reason, I'm not getting FTTT for III.

F -->F = T

Answer 15

i'm using ~q-->~p

Answer 16

ok.

Answer 17

so my III is TTTT

Answer 18

that's not right

Answer 19

TFTT?

Answer 20

I keep getting TFTT.

Yes. That looks correct.

Answer 21

Is that also what you got for II?

Answer 22

F-->F = T?

Answer 23

Correct. It's a little weird, but that is true.

Answer 24

ok. II, III equiv

Answer 25

That's also what I'm getting.

Answer 26

cool thanks

Answer 27

You're welcome. I've got to go now, so good luck with the rest of your problems.

Answer 28

thanks so much!