I am having a lot of trouble with word problem questions. 
If someone could help me that would be great. If you could 
show your work so that I can understand how you got the 
answer would be apprectiated. Thanks so much! 

1.  (4pts) 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 

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(a) p /\ q

The symbol /\ means "AND", so you write statement p, then "AND", the
statement q:

Roses are red AND the sky is blue

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(b) p /\ (q \/ r) 

The symbol /\ means "AND", and the symbol \/ means "OR",

Roses are red AND (the sky is blue OR the grass is green) 

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(c) q -> (p /\ r)

The symbol -> means to put the word "IF" in front of the first statement
and "THEN" in front of the second:

IF q THEN (p /\ r)

or

IF roses are red, THEN (the sky is blue OR the grass is green)

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(d) (~r /\ ~q) -> ~p 

The ~ means NOT, so

(NOT r AND NOT q) ->  NOT p

Then for the -> we put IF in front of the first and
THEN in front of the second:

IF (NOT r AND NOT q) THEN  NOT p

Now we can substitute for the letters:

"NOT r" can be written "The grass is NOT green"
"NOT q" can be written "The sky is NOT blue"
"NOT p" can be written "Roses are NOT red"

So we have:

IF (the grass is NOT green AND the sky is NOT blue) THEN roses are NOT red.

Edwin