Determine which, if any, of the three statements are equivalent. Give a reason for your
conclusion. Show complete work and submit your solution to the Dropbox.
I) If the garden needs watering, then the garden does not need weeding.
II) Either the garden needs watering or the garden does not need weeding.
III) If the garden does not need watering, then the garden does not need weeding.
a. None are equivalent
b. I, II, and III are equivalent
c. I and II are equivalent
d. I and III are equivalent
e. II and III are equivalent
Solution
garden needs watering->p,garden does not need watering->-p garden does need weeding->q
,garden does not need weeding->-q statement p q -p -q P->-q pv-q -p->-q 1 T T F F F 2 T T F F
T 3 T T F F T e. II and III are equivalent