Question

use the equivalency

\\(\sim(p \wedge q) \equiv \sim p \vee \sim q\\)

to select the statement that is logically equivalent to ...

\it is not true that north dakota is a state and east dakota is a state.\

• north dakota is not a state, and east dakota is a state.
• east dakota is a state, or north dakota is not a state.
• north dakota is a state, or east dakota is not a state.
• north dakota is not a state, and east dakota is not a state.
• north dakota is not a state, or east dakota is not a state.

Explanation:

Define propositional variables

$$
LATEXBLOCK0
$$

Translate the given statement

$$ \sim(p \land q) $$

Apply De Morgan's Law

$$
LATEXBLOCK1
$$

Answer:

• North Dakota is not a state, and East Dakota is a state.
• East Dakota is a state, or North Dakota is not a state.
• North Dakota is a state, or East Dakota is not a state.
• North Dakota is not a state, and East Dakota is not a state.
• North Dakota is not a state, or East Dakota is not a state. (Correct answer)