Respuesta :
Correct order of question is;
Consider the following statements:
p: Niagara Falls is in New York.
q: New York City is the state capital of New York.
r: New York City has more than 40 inches of snow in 2525.
The statement p is true, and the statement q is false. Represent each of the following by a formula. What is their truth value if r is true? What if r is false?
(a) If Niagara Falls is in New York, then New York City is the state capital of New York. statements by a formula.
(b) Niagara Falls is in New York only if New York City will have more than 40 inches of
(c) Niagara Falls is in New York or New York City is the state capital of New York implies that New York city will have more than 40 inches of snow in 2525
(d) For New York City to be the state capital of New York, it is necessary that New York city would have more than 40 inches of snow in 2525
(e) For Niagara Falls to be in New York, it is sufficient that New York City will have more than 40 inches of snow in 2525
Answer:
A) p⇒q is false
B) p⇒r is false if r is false
C) (p V q) ⇒r is false is r is false
D) q⇒r is true whether or not r is true or false.
E) r⇒p is true whether or not r is true or false.
Step-by-step explanation:
We are given;
p: Niagara falls is in Now york to be true
q: New york city is the slate capital of New york to be False
r: New York city will have more than 40 inches of snow in 2525.
A) it's trying to say that if p is true, then q is true. But from the given statements, it doesn't follow because we are told p is true and q is false. Thus, we can write it as;
p⇒q is false
B) They are trying to suggest that p is true when r is true.
From given statements, p is true but r could either be true or false. Thus, we can write this as;
p⇒r is is true if r is true
Also, p⇒r is false if r is false
C) The statement implies that;
(p V q) ⇒r. However, again since r could either be false or true, we can say that;
(p V q) ⇒r is true if r is true
And (p V q) ⇒r is false is r is false
D) This statement suggests that q is true with r being true.
This can be written as;
q⇒r is true whether or not r is true or false.
E) This statement suggests that for r to be true, then p is true.
Thus;
r⇒p is true whether or not r is true or false.
