SOLUTION: State eache of thefollwing in words and determind the truth value of each a)¬p v q b)¬q ⇒¬p

Question 1177227: State eache of thefollwing in words and determind the truth value of each
a)¬p v q
b)¬q ⇒¬p
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's break down each statement:
**Given:**
* p: "The sun is shining."
* q: "It is raining."
**a) ¬p ∨ q**
* **In words:** "The sun is not shining, or it is raining."
* **Truth value:**
* To determine the truth value, we need to consider the individual parts:
* ¬p: "The sun is not shining."
* q: "It is raining."
* The "∨" symbol represents "or," which is true if at least one of the statements is true.
* Therefore, the statement is true if either the sun is not shining, or it is raining, or both. We can not give a definitive true or false without knowing the current state of the sun and rain.
* Thus we say that the truth value is dependent on the actual truth values of p and q.
**b) ¬q ⇒ ¬p**
* **In words:** "If it is not raining, then the sun is not shining."
* **Truth value:**
* To determine the truth value, we need to consider the individual parts:
* ¬q: "It is not raining."
* ¬p: "The sun is not shining."
* The "⇒" symbol represents "implies" or "if...then."
* An implication is only false when the antecedent (the "if" part) is true and the consequent (the "then" part) is false.
* In this case, the statement is saying that the absence of rain implies the absence of sunshine. This is not necessarily true in the real world (the sun can be shining without rain, and the sun can be not shining without rain, and the sun can be not shining when it is raining).
* Like the previous statement, the truth value is dependent on the actual truth values of p and q.
**Summary:**
* Both statements' truth values depend on the actual truth values of the propositions "The sun is shining" (p) and "It is raining" (q).
* In short, without knowing if it is raining or if the sun is shining, we can not assign a definitive true or false to either statement.

RELATED QUESTIONS
If p is false and q is true, determine the truth value of the following: a) ~(p ^... (answered by Edwin McCravy,Aldorozos)

a) Construct a truth table for (p^~q)V(~pVq). What is the truth value of the statement if (answered by stanbon)

Determine the truth value of the following statement if (a) p is true, q is false, and r (answered by solver91311)

construct the truth table for each of the following statements.... (answered by MathLover1)

p is False and q is False. Determine the truth-value of the following compound statement: (answered by jim_thompson5910)

HELP Determine the truth value of the statement ~q arrow [ ~ r v (revered) (p v q)]... (answered by MathLover1)

Let p represent a true statement, while q and r represent false statements. Fing the... (answered by jim_thompson5910)

Fill in the truth table for ~p V q p | q | ~ p | ~ p V q _|__ |____ |_________ (answered by Edwin McCravy,jim_thompson5910)