If Then Statements!!! AGAIN!!!!
The Statement - If P then Q
Converse or P and Q flipped - If Q then P
NEW INFO ALERT
Inverse or the Not statement – If NOT P Then NOT Q.
Contropositive or the Not Converse – If NOT Q Then NOT P
Logical Equivalence
- A statement and it’s Contrapositive are Logically Equivalent
- A statement is NOT Logically Equivalent to it’s Converse and Inverse.
- Similar to an = and the biconditional
- Results of either
Both True
Both False
Examples of everything above :
True conditional : If two lines are not coplanar, then they do not intersect.
Inverse of it : If two lines are coplanar, then they intersect. (false)
Contropositive : If two lines intersect, then they are coplanar. (True)
Venn Diagrams!!!
You use Venn diagrams to represent conditionals. You Use Venn Diagrams/Truth Tables to determine Logical Equivalence.
BUT HOW!!?! You might ask. Well I’m getting to that. It’s easiest to use
EXAMPLES :
G: all runners are athletic.
P: Leroy is a runner.
C: Leroy is an athlete.
HOW DID I JUST DO THAT!
Well it is quite simple you use the Venn Diagram ( Since Ms.Hunt doesn’t want us using the Truth tables since they will confuse us).
The P is runners and the Q is Athletic. So then what is Leroy? Leroy is a runner as given so he goes in the Runner section or Q. and Q is inside of P. Since in the given.
Then it is quite obvious that Leroy is an Athlete since he is also in the P section.
Or you can look at the given info and see that runners are athletes and Leroy is a runner making him an athlete. TRANSITIVE PROPERTY!!
MORE EXAMPLES : With INVERSES
P: Lucia is NOT an Athlete
C: Lucia is NOT a runner
The conclusion is true. We are still using the same given as the previous Question/ Example.
The reason Lucia is not an athlete is because She is neither in the runner circle nor the Athlete circle so she is a lame-o.
And that’s all folks! Here is one helpful video one funny video and an amazing link to tons of awesome info!
http://www.blinkx.com/watch-video/g1d-converse-inverse-and-contrapositive/z_3OtHw6mD_ALGPXFjtUZQ
http://vimeo.com/15367677
http://accgeo435.blogspot.com/
And the NEXT SCRIBE IS!!!!!!!!!!!
Well uh....
Almost there....
If Not Phil J, then it is not Ms.Hunt
If not Ms.Hunt, then is is not David.
If not David then it is not Francis
If not any other person but one, then it's..............
KATIE HAHAHAHAHAH!!!!
you always try to pick katie, matthew. with that information, i can make a conditional
ReplyDeleteIf Matthew is the scribe, he will try to pick Katie. TRUE
Conv: If Katie was picked for the scribe, then Matthew was the scribe. FALSE
Inv: If Matthew is not the scribe, then he will not try to pick Katie. TRUE
Contr: If Katie was not picked for the scribe, then Matthew was not the scribe. FALSE