SOLUTION: Let p, q, and r be the following statements: p: Roses are red q: The sky is blue r: The grass is green Translate the following statements into English (a) p and q

Question 178551This question is from textbook
: Let p, q, and r be the following statements:
p: Roses are red
q: The sky is blue
r: The grass is green
Translate the following statements into English
(a) p and q (b) p and (q or r) (c) q if then (p and r) (d) ( Not r and not q) if then, not p
Do I understand this correctly??
(a) p and q would be: roses and sky are blue??? help me please.... This question is from textbook

Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started.

a)

p and q ... Start with the given expression

(roses are red) and (the sky is blue) ... replace "p" with the statement "roses are red" and replace "q" with "the sky is blue"

So p and q translates to: "roses are red and the sky is blue"

----------------------------------------------------

b)

p and (q or r) ... Start with the given expression

(roses are red) and (q or r) ... Replace "p" with the statement "roses are red"

(roses are red) and ((the sky is blue) or r) ... Replace "q" with the statement "the sky is blue"

(roses are red) and ((the sky is blue) or (the grass is green)) ... Replace "r" with the statement "the grass is green"

So p and (q or r) translates to: "roses are red and the sky is either blue or the grass is green"

Note: I threw in the term "either" to show that there is grouping
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

No.

a). :

Roses are red and the sky is blue.

b). :

Roses are red and at least one of the following statements is true: the sky is blue or the grass is green.

c). :

If the sky is blue then both of the following statements are true: 'roses are red' and 'the grass is green.'

d). :

If both of the statements 'roses are not red' and 'the sky is not blue' are true, then roses are not red.

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