Answer to Question #92890 in Discrete Mathematics for as

Question

If the domain is the set of words {violet, indigo, blue, green, yellow, orange, red}, which of the following sentences is/are true?


(P)∀x(if x does not contain the letter ‘e’, then x contains the letter ‘n’)
(Q) ∃x(if x contains the letter ‘e’, then x contains at most 4 letters)

(R) ∀x(if x contains more than 5 letters, then x contains the letter ‘o’)

Answer 1

All statements P, Q, R are true.

P - there's only word indigo, which doesn't contain letter e and it contains n, so statement is true.

Q- word x=blue.

R - words with more than five symbols are indigo, orange, yellow, violet; they all contain letter o.