Question

Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion. Show complete work.

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.
a. I, II, and III are equivalent
b. I and II are equivalent
c. I and III are equivalent
d. II and III are equivalent
e. None are equivalent

Answer 1

let boat leaking be B
let mary seated be S
not leaking is -B
not seated is -S
1) if B, then -M
ll) if B, then M
obviously not the same
lll) if -M, then -B
at first the last may look the same as ll) except with negatives.
so using truth tables
1)B M is only false if B is true and M is false.
ll)B -M is false for whenever B is true and M is true
iii)-M B is false when B and M are false.
so none of them are the same.