Posted by Jen on Friday, July 29, 2011 at 10:45pm.
Form the converse: If I do not mow the lawn, then the grass grows too tall.
Is it:
If the grass does not grow too tall, then I did not mow the lawn??

Math  MathMate, Friday, July 29, 2011 at 11:00pm
Here is list of the four possibilities (source: (Broken Link Removed)
* statement: if p then q
* converse: if q then p
* inverse: if not p then not q
* contrapositive: if not q then not p
Your proposition is not one of them.
Let
p=I don't mow the lawn
q=grass grows too tall
The original statement is then
if p then q
The converse: if q then p
i.e. if the grass grows too tall, then I didn't mow the lawn.
You have proposed: if ~q then p
"If the grass does not grow too tall, then I did not mow the lawn" which is not one of the four usual variations.

Math  Jen, Friday, July 29, 2011 at 11:08pm
so its:
If the grass grows too tall, then I did not mow the lawn??

Math  MathMate, Friday, July 29, 2011 at 11:11pm
Correct.

Math  Jen, Friday, July 29, 2011 at 11:15pm
yay! i get it now :) thanks!

Math :)  MathMate, Friday, July 29, 2011 at 11:22pm
You're welcome!
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