Consider the following statements: p: Niagara Falls is in New York. q: New York
ID: 3009755 • Letter: C
Question
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 will have more than 40 inches of snow in 2525.
The statement p is true, and the statement q is false. Represent each of the following statements by a formula. What is their truth value if r is true? What if r is false?
(a) Niagara Falls is in New York if and only if New York City is the state capital of New York.
(b) Niagara Falls is in New York iff New York City will have more than 40 inches of snow in 2525.
(c) Niagara Falls is in New York or New York City is the state capital of New York if and only if New York City will have more than 40 inches of snow in 2525.
Explanation / Answer
(a) q => p
(b) r => p
(c) r => p U q
If r is true, it doesnt have effect on (a), but if r is true, both (b) and (c) are true and if r is false, both (b) and (c) are false.