# if then statements

• Oct 24th 2010, 08:22 AM
DarK
if then statements
Say I have the statement: "None of the unnoticed things, met with at sea, are mermaids. "

Lets say: M = set of mermaids
N = set of things noticed

If I wanted to convert this into an if then statment, would it be:

M --> N (if it is a mermaid, then it is noticed)

or

N --> M (if it is noticed, then it is a mermaid)

How do I know which is the correct if-then statement?

Any help is appreciated!
• Oct 24th 2010, 08:30 AM
Jhevon
Quote:

Originally Posted by DarK
Say I have the statement: "None of the unnoticed things, met with at sea, are mermaids. "

Lets say: M = set of mermaids
N = set of things noticed

If I wanted to convert this into an if then statment, would it be:

M --> N (if it is a mermaid, then it is noticed)

or

N --> M (if it is noticed, then it is a mermaid)

How do I know which is the correct if-then statement?

Any help is appreciated!

think of the statement this way: if it is an unnoticed thing met at sea, then it is NOT a mermaid. (since no such thing is a mermaid)

now what do you think the answer is?
• Oct 24th 2010, 08:48 AM
DarK
I think I got the statements in my first post mixed up with their contrapositives.

Well, I have

~N -- > ~M
(if it is unnoticed then it is not a mermaid)

Again I'm a little confused, why can't I have it as:

~M --> ~ N
(if it is not a mermaid then it is unnoticed)

Thank you.
• Oct 24th 2010, 10:13 AM
Jhevon
Quote:

Originally Posted by DarK
I think I got the statements in my first post mixed up with their contrapositives.

Well, I have

~N -- > ~M
(if it is unnoticed then it is not a mermaid)

Again I'm a little confused, why can't I have it as:

~M --> ~ N
(if it is not a mermaid then it is unnoticed)

Thank you.

your first implication is correct. and note that your second is its converse. it is not always true that the converse of a true implication is true. the converse is equivalent to N --> M, so you are saying that if it is noticed, it's a mermaid. clearly this isn't true, there are tons of things at sea that you notice that are not mermaids.