Question

Are the two statements logically equivalent? Why or why not?

(~p ∧ q) and (~p ∨ q)

Answer 1

~p ^ q= \(\text{not p and q}\)
~p ∨q= \(\text{not p or q}\)

Answer 2

@happykiddo do you get it?
^ = and
∨= or

Answer 3

yeah i got that

Answer 4

Great:D Let me know if you have any doubt anywhere:D

Answer 5

if p=t and q=t,
~p^q=f^t=f
~pvq=fvt=t, so the statements are not equivalent

Answer 6

so they wouldnt be logically equivalent because there seperated by an "and" in the middle??

Answer 7

no, they are not logically equivalent, because there exist such arguments, that statements with these arguments gives different values.

Answer 8

hhmmm staarting to get ill go and look over the lesson again :) thanks

Answer 9

you can check directly by writing the truth table for both and seeing if they are identical

Answer 10

on the other hand, as mathmagician wrote, it would be a miracle if they were equivalent, because that would mean "and" meant the same thing as "or" which is certainly does not