Q:

Use De Morgan’s laws to write negations to the following statements:1. The train is late or my watch is fast.2. Dogs bark and cats meow.

Accepted Solution

A:
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∧ = and1. 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"