Calculus questions......................1. (4pts) Let p, q, and r be the following statements:?

Question

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

(a) p ∧ q (b) p ∧ (q ∨ r) (c) q → (p ∧ r) (d) ( ~ r ∧ ~ q) → ~ p

2. (4pts) Write in symbolic form using p, q, r, ~, →, ∨, ∧, where p, q, r represent the following statements:

p: A puppy is green-eyed

q: A puppy can be taught

r: A puppy loves toys

If a puppy is green-eyed, then it cannot be taught
If a puppy cannot be taught, then it does not love toys
If a puppy loves toys, then either the puppy can be taught or the puppy is green-eyed.
If the puppy is not green-eyed, then the puppy loves toys and the puppy can be taught.

Answer 1

If there are points being awarded for this, as the question suggests, then you shouldn't be asking it here, because that would be cheating.

Answer 2

The ^ symbol means "and"; the "v" symbol means OR.
The arrow means "If ... then" and the ~ means "not".

(a) Roses are red and the sky is blue.
(b) Roses are red and either the sky is blue or the grass is green.
(c) If the sky is blue, then roses are red AND the grass is green.
(d) The grass is NOT green AND the sky is NOT blue.

2)

(a) p -> ~q
(b) ~q -> ~r
(c) r -> (p v q)
(d) ~p -> (r ^ q)