Question

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.

Answer 1

2

Explanation:

Answer 2

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.

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"