Question

determine which, if any, of the 3 statements are equivalent:
I. If the pipe is leaking, then I will not call the roofer.
II. It is not the case that the pipe is leaking and i will call the roofer
III. Either the pipe is not leaking or i will not call the roofer.

Answer 1

Here, the tricky part is figuring out how to write these statements in mathematical terms.

So, let
p="The pipe is leaking"
q="I will call the roofer"

Answer 2

ok

Answer 3

With these you can set up your formulas

I. (p --> ~q)
II. (~p ^ q)
III. (~p V ~q)

Now you have to draw a truth table for each of these, and determine which of them are the same.

Answer 4

so far I, II are equivalent. working on III

Answer 5

I'm not getting that I and II are equivalent.

Answer 6

hmmm.. i got that all three were equivalent

Answer 7

so, I. (p --> ~q) would be F,T,T,T on the ---> column?

Answer 8

Yes.

Answer 9

I'm getting that I and III are equivalent, but not II.

Answer 10

ok. here's what i got for II.
OH. i did a T^T as false. that was my mistake

Answer 11

So what are you getting for II now?

Answer 12

F,F,T,F

Answer 13

That looks correct.

Answer 14

Good job.

Answer 15

thanks.