Answer to Question #239629 in Discrete Mathematics for enKay

Question

A) Let P be the propositions Roses are Red and Q be the propositions Violets are Blue.
Express each of the following propositions as logical expressions:

(I) If roses are not red, then violets are not blue.

(II) Roses are Red or Violets are not blue.

(III) Either Roses are Red or Violets are Blue (but not both)

Answer 1

Let $P$ is "Roses are Red", $Q$ is "Violets are Blue".

(I) $\neg P\implies \lnot Q$ is "If roses are not red, then violets are not blue."

(II) $P\lor \lnot Q$ is "Roses are Red or Violets are not blue. "

(III) $(P\lor Q)\land \lnot(P\land Q)$ is "Either Roses are Red or Violets are Blue (but not both)"