Question

Determine which, if any, of the three statements are equivalent.
I) If I am hungry, then I will not be able to concentrate at the meeting.
II) Either I am not hungry or I will be able to concentrate at the meeting.
III) If I am able to concentrate at the meeting, then I am not hungry.

I, II, and III are equivalent
I and II are equivalent
II and III are equivalent
I and III are equivalent
None are equivalent

Answer 1

Let P = I am hungry
Q = I will not be able to concentrate at the meeting

The equivalent statement is ~Q -> ~P
Do you see a match?

Answer 2

no

Answer 3

~Q looks like: I am able to concentrate at the meeting
~P looks like: I am not hungry
Yes?

Answer 4

none are equivalent then?

Answer 5

So I used the statements in I and assigned them to P and Q and say that I means that P -> Q. Then I negated P and Q. The classic equivalent of P -> Q is ~Q -> ~P. Then I notice that the statements in III match ~Q -> ~P. So I and III seem to match. The remaining question is whether II matches...

Answer 6

Doyou follow that?

Answer 7

yea

Answer 8

For the last part, II says first either I am not hungry .. OK
or (I am hungry) and I will be able to concentrate at the meeting
so we have some new statement OR another statement that contradicts I.

Answer 9

another statement that contradcts

Answer 10

So I think I and III are equivalent and II is not. OK with that?