Using DeMorgan’s rule, state the negation of the statement

Question

Using DeMorgan’s rule, state the negation of the statement: “The car is out of gas or the fuel line is plugged.”

Let C stand for “The car is out of gas” and let F stand for “the fuel line is plugged”. then the answer is $(\lnot C\lor \lnot F) \equiv \lnot C\land \lnot F.$

Answer 1

Using DeMorgan’s rule, state the negation of the statement: “The car is out of gas or the fuel line is plugged.”

This statement is a disjunction; that is an 'or'-joined statement. Conjunctions are the 'and'-joined statement.

DeMorgan states: The negation of a disjunction is the conjunction of negations.

The negation is thus: "The car is not out of gas and the fuel line is not plugged."

Answer 2

Start with the original statement, which according to your key, is:$$C\lor F$$

Now negate this, and then apply DeMorgan's:

$$\lnot(C\lor F) \equiv \lnot C \land \lnot F$$

So the negation of the given sentence translates to:

"The car is not out of gas, and the fuel line is not plugged."

Try to understand the logic behind DeMorgan's and what the negation of a disjunction means