Answer: The negations are:
1. The train is not late and my watch is not fast.
2. Dogs don't bark or cats don't meow.
Step-by-step explanation:
Hi!
De Morgan's laws for two propositions P and Q are:
1. ¬(P ∨ Q) = (¬P) ∧ (¬Q)
2. ¬(P ∧ Q) = (¬P) ∨ (¬Q)
where the symbols are,
¬ = not
∨ = or
∧ = and
1. In this case the proposition is P ∨ Q, with
P = "the train is late"
Q = "my watch is fast"
Then by law 1: ¬(P ∨ Q) = "The train is not late and my watch is not fast"
2. In this case the proposition is P ∧ Q, with
P = "dogs bark"
Q = "cats meow"
Then by law 2: ¬(P ∧ Q) = "Dogs don't bark or cats don't meow"
