Question

Use De Morgan's laws to write an equivalent statement for the sentence. The bus does not have an engine or the people do not have money.

Which statement is equivalent to the given sentence?

A. It is false that the bus has an engine and the people have money.

B. The bus has an engine and the people have money.

C. It is false tht the bus has an engine or the people have money.

D. The bus has an engine and the people do not have money.

Please show work legibly as I do not see well.

Answer 1

A. It is false that the bus has an engine and the people have money.

Explanation:

Given statement is -

The bus does not have an engine or the people do not have money.

The De Morgan's laws states that the complement of the union of two given sets is the intersection of their complements.

Also, the complement of the intersection of these two sets is the union of their complements.

negative (p ∨ q)⇔ p ∧ negative q

So, here option A is correct. It is false that the bus has an engine and the people have money.