If and only if?

Question

Is the statement true or false?

New Jersey is a state if and only if Florida is not a state?

Florida is a state?

So that will be false?

Is this the way it works?

It's a different statement than "New Jersey is a state AND Florida is not a state." — Frenzy Li, Jul 27 '13 at 12:08

score 3 · Answer 1 · answered Jul 27 '13 at 11:56

3

An "if and only if" statement is true according to whether the truth values of the two statements match. Here, they do not match, so the statement is false.

answered Jul 27 '13 at 11:56

Eric Auld

28,127

score 1 · Answer 2 · answered Jul 27 '13 at 12:00

The statement "New Jersey is a state if and only if Florida is not a state", is the same thing as saying, "$\,$'If New Jersey is a state then Florida is not a state' and 'if Florida is not a state then New Jersey is a state'$\,$".

Since the statement, "if New Jersey is a state then Florida is not a state" is false, the original statement is false too.

If and only if?

2 Answers2