Which of the following is the negation of a disjunction?
A) It is not the case that Joseph is late for work.
B) Joseph was on time for work every day last month.
C) It is not true that both Joseph is late for work and that Joseph owes me money for gas.
D) It is not the case that either Joseph is late for work or that he owes me money for gas.
E) If Joseph is not late for work one more time, then he will keep his job.

Question

Quizplus · Accepted Answer

The negation of a disjunction is the statement that neither of the disjuncts is true. Choice D says "It is not the case that either Joseph is late for work or that he owes me money for gas," which is the same as saying that Joseph is not late for work and he does not owe me money for gas. This is the negation of the disjunction "Either Joseph is late for work or he owes me money for gas."

Which of the Following Is the Negation of a Disjunction