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 this course covers logic and it covers finance.\

this course covers finance, or this course does not cover logic.
this course covers logic, or this course does not cover finance.
this course does not cover logic, and this course does not cover finance.
this course does not cover logic, or this course does not cover finance.
this course does not cover logic, and this course covers finance.

Explanation:

Define the propositional variables

$$
LATEXBLOCK0
$$

Translate the given statement into symbolic form

$$ \sim(p \wedge q) $$

Apply De Morgan's Law to find the equivalent statement

$$
LATEXBLOCK1
$$

Answer:

• This course covers finance, or this course does not cover logic.
• This course covers logic, or this course does not cover finance.
• This course does not cover logic, and this course does not cover finance.
• This course does not cover logic, or this course does not cover finance. (Correct answer)
• This course does not cover logic, and this course covers finance.