Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 17, 2023

Use De Morgan's laws to write an equivalent statement to " $\neg (4:00 \vee \text{time to go})$ ". Choose the correct answer: B. $\neg 4:00 \wedge \neg \text{time to go}$

STEP 1

Assumptions
1. De Morgan's laws state that the negation of a disjunction (OR) is equivalent to the conjunction (AND) of the negations.
2. The original statement is a negation of a disjunction.
3. The disjunction is "It is $4:00$ OR it is time to go."
4. We want to find an equivalent statement using De Morgan's laws.

STEP 2

Write down the original statement using logical notation.
$\neg (A \lor B)$
where $A$ is "It is $4:00$ " and $B$ is "It is time to go".

STEP 3

Apply De Morgan's laws to the original statement.
According to De Morgan's laws:
$\neg (A \lor B) \equiv (\neg A \land \neg B)$

STEP 4

Translate the logical notation back into a verbal statement.
The equivalent statement to $\neg (A \lor B)$ using De Morgan's laws is:
"It is not $4:00$ AND it is not time to go."

STEP 5

Match the equivalent statement to the correct answer from the given options.
The correct answer is:
A. It is not 4:00 and it is not time to go.

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