If I have the following statements
p: It is cold outside
q: It is snowing
p∧q = It is cold outside, and it is snowing.
p∨q = It is either cold outside or it is snowing.
If I were to negate p∧q would it be written like this ~(p∧q)? and in sentence form i would say "It is not cold or it is not raining" since de Morgan's laws say ~(p∧q) is equivalent to ~p∨~q?
Likewise for the second statement, for ~(p∨q) I would say "It is not cold outside and it is not snowing." since de Morgan's laws say ~(p∨q) is equivalent to ~p∧~q?
I'm just confused about whether I am interpreting this correctly.
Best Answer
Yes, you are interpreting it correctly, and your justification (as applications of DeMorgan's Laws) is spot on.
$$\lnot (p\land q) \equiv \lnot p \lor \lnot q$$
This can be interpreted: "It is not the case that it is both cold and snowing" which is equivalent to the statement "It is not cold, or it is not snowing."
$$\lnot(p \lor q) \equiv \lnot p \land \lnot q$$
This can be interpreted as "It is not the case that it is either cold or snowing," which is equivalent to stating "It is not cold and it is not snowing."