If p stands for this meal is delicious and q stands for busy people do not eat, write each of the following in symbolic form. Use this information to answer parts a through c. (A)This meal is delicious. (B)busy people do not eat or this meal is not delicious
A) p
B) Either-or probabilities are found by adding the individual probabilities. p + c
C) no see C, sí ?
a. p
b. (q OR NOTp) I cant type OR symbol, and the overscore for NOT
(A) p
(B) q or ~p
To write the given statements in symbolic form, we can use the following symbols:
- p: This meal is delicious
- q: Busy people do not eat
Now, let's write each of the given statements in symbolic form:
(A) This meal is delicious: p
(B) Busy people do not eat or this meal is not delicious: q ∨ ¬p
Now, let's answer parts (a) through (c):
(a) If the meal is not delicious, or busy people do not eat, then the statement "p → (q ∨ ¬p)" represents this relationship.
(b) To determine the truth value of the statement "p → (q ∨ ¬p)," we consider all possible cases:
- If p is true (meal is delicious), then the statement simplifies to "True → (q ∨ ¬True)" or "True → (q ∨ False)" which is always True.
- If p is false (meal is not delicious), then the statement simplifies to "False → (q ∨ ¬False)" or "False → (q ∨ True)" which is always True.
Therefore, the statement "p → (q ∨ ¬p)" is always True.
(c) To determine the truth value of the given statement "¬p ∨ q," we consider all possible cases:
- If p is true (meal is delicious), then "¬p" is false, and the statement simplifies to "False ∨ q" which is always equal to the value of q.
- If p is false (meal is not delicious), then "¬p" is true, and the statement simplifies to "True ∨ q" which is always True.
Therefore, the statement "¬p ∨ q" is always true.