Question

Please help, trying to get the knack for negating down early in the quarter so I don't have problems later....The domain of the following predicates is the set of all plants.
P(x) = "x is poisonous."
Q(x) = "Jeff has eaten x."
Translate the following statement into predicate logic.
Jeff has never eaten a poisonous plant.

Answer 1

There does not exist a plant such that the plant is poisonous and Jeff has eaten it

this is equivalent to

there does not exist x such that P(x) and Q(x)
using E = exist

~ (E x s.t. P(x) & Q(x) )

Answer 2

`~ (E x s.t. P(x) & Q(x) )`

is equivalent to , if you distribute the negation sign

`For all x ~( P(x) & Q(x) )`

`For all x (~P(x) or ~ Q(x))`

since (~p or ~q) = p -> ~q

`For all x ( if P(x) then ~Q(x))`

In other words, to bring it back to english:

for all plants , if the plant is poisonous then Jeff did not eat it.

this is also equivalent by similar reasoning

for all plants, if Jeff ate it then it is not poisonous