Let A, B, and C be the following statements: A = Roses are red. B = Violets are

Question

Let A, B, and C be the following statements: A = Roses are red. B = Violets are blue. C = Sugar is sweet. Part i) Use A, B, C as defined above to translate the following statements into English. a. B -C b. B (A rightarrow X) c. C ( A doubleheadarrow B) d. (C A) doubleheadarrow B e. (B C) rightarrow A f. A (B C) g. (A B) C Part ii) Translate the following compound statements into symbolic logic notation. a. Roses are red and violets are blue. b. Roses are red, and either violets are blue or sugar is sweet but not both. c. Whenever violets are blue, roses are red and sugar is sweet. d. Roses are red only if violets aren't blue or sugar is sour. f. sugar is sour, then either violets aren't blue or sugar is sweet.

Explanation / Answer

a) Violets are blue or sugar is not sweet    or   Violets are blue or sugar is sour

b)Violets are not blue or if roses are red then sugar is sweet

c) Sugar is sweet and roses are not red if and only if violets are blue

d)Sugar is sweet and roses are not red is necessary and sufficient for violets are blue

e) If it is not the case that violets are blue and sugar is not sweet then roses are red

f) roses are red or, violets are blue and sugar is not sweet

g)roses are red or violets are blue, and sugar is sweet

II) a) A^B

b) A ^ (B v C)

c) B -> (A ^ C)

d) A -> (~B v ~C)

e) A ^ ( ~C -> ( ~B v C))

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