Contrapositive of a conditional statement
A conditional statement is one which has a hypothesis and a conclusion in the if-then format. So, for example, "If an angle is 45 degrees, then the angle is acute."
The converse of a conditional statement is where you switch the hypothesis and conclusion literally. From the same example, "If the angle is acute, then the angle measures 45 degrees."
Obviously, the converse is a false statement; an acute angle can measure 30 degrees, doesn't have to be 45.
A statement whose converse and original statement are both true statements is a biconditional statement.
My Example: If it is December 25th, then it is Christmas Day.
If it is Christmas Day, then it is December 25th.
Your turn!! (be careful. Make sure it is biconditional!)
if it is light out then it is day.
ReplyDeleteif it is day then it is light out.
Unless you're in Northern Alaska in July. There, the sun is out at midnight, technically nighttime, even though "it is light out."
DeleteIf you are a human, then you have feet
ReplyDeleteIf you have feet ,then you are human
This does not sound like a biconditional statement
DeleteI believe chimpanzees have feet
DeleteConditional: If I play volleyball, then I am an athlete
ReplyDeleteConverse: If I am an athlete, then I play volleyball
Biconditional: If I am going trick-or-treating, then it is Halloween
If it is Halloween, then I am going trick-or-treating
Good, Mallory.
DeleteIf two angles add to 90 degrees, then they are complementary.
ReplyDeleteIf something is complementary, then the two angles add to 90 degrees.
Something is complementary if and only if the the angles add to 90 degrees.
Well done, Jake. "If and only if" is indeed what makes up a biconditional statement.
DeleteConditional: If I have a quarter horse, then I am a barrel racer.
ReplyDeleteConvers: If I am a barrel racer, then I have a quarter horse.
Biconditional: If I am collecting colored eggs, then it is Easter.
If it is Easter, then I am collecting colored eggs.
You don't necessarily collect colored eggs on Easter. It has to define Easter.
DeleteIf the dog has spots, it's a Dalmatian
ReplyDeleteIf it it a Dalmatian, the dog has spots
A Dalmatian is the only spotted dog?
DeleteIf he can drink alcohol, then he is over twenty.
ReplyDeleteIf he is over twenty, then he can drink alcohol.
21, but yes (assuming you're in the U.S. of course.
DeleteIf I am a runner then, I run regularly.
ReplyDeleteIf I run regularly, then, I am a runner.
Good, Allie.
DeleteIf I do my hair, I am a hairstylist.
ReplyDeleteIf I am a hairstylist, I do my hair.
I feel like you can do your hair without being a 'stylist', but you've got the right idea, Abby.
Deletebi conditional: If the gators played a game they won.
ReplyDeleteIf the gators won they played a game.
Maybe when Tebow was your QB. That's hilarious. I guess that UM defeat got washed from your memory.
DeleteIf it is 6th period, then I am enrolled in study hall.
ReplyDeleteIf I am enrolled in study hall, then it is 6th period.
if a skater lands a kick-flip he or she is happy
ReplyDeleteIf a skater is happy they landed a kick-flip
If an animal has fur, then it is a mammal.
ReplyDeleteIf the animal is a mammal, then it has fur.
if i have thumbs, i am a human
ReplyDeleteif i am a human, i have thumbs
if he can drive a car he is 16 or older
ReplyDeleteif he is 16 or older he can drive a car
if he is fishing, then he has a fishing license.
ReplyDeleteif he has a fishing license, then he can fish.
If she can drink soda, she has soda.
ReplyDeleteIf she has soda, she can drink soda.
If I am reading for fun, then I am done with my homework.
ReplyDeleteIf I am done with my homework, then I can read for fun.
if i am playing xbox, then i have finished my homework.
ReplyDeleteIf i am done with my homework, then i am playing xbox
If i am moving, i am in motion.
ReplyDeleteIf i am in motion i am moving
If I play a sport, then I am an athlete
ReplyDeleteIf I am an athlete, I play a sport.
If I am sick then I am sad
ReplyDeleteIf I am sad I am sick
if i am on the computer i have nothing to do,
ReplyDeleteif i have nothing to do then im on the computer.
If I am happy then I am in the sun.
ReplyDeleteIf I am in the sun then I am happy.
If I am tired then it's morning
ReplyDeleteIf it's morning then I'm tired
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ReplyDeleteIf I eat pizza, I am hungry
ReplyDeleteIf I am hungry, then i eat pizza
if i run i get hungry
ReplyDeleteif i am hungry i just ran
If I'm playing sports then school is over
ReplyDeleteIf school is over then I am playing sports
If I'm in the swimming pool I'm wet
ReplyDeleteIf I'm wet I'm in the swimming pool
If its December 31st it is new years eve if it is new years eve it is December 31st
ReplyDeleteIf i drank coke then im thirsty
ReplyDeleteIf i'm thirsty i drank coke
If i drank coke then im thirsty
ReplyDeleteIf i'm thirsty i drank coke
If i'm confused, i'm thinking.
ReplyDeleteIf i'm thinking, i'm confused.
If it is october 31 than it is halloween
ReplyDeleteIf it is halloween than it is October 31
If I am lazy, I wear sweat pants
ReplyDeleteIf I wear sweatpants, I am lazy
If I get an "a" in class, I'm smart
ReplyDeleteIf I'm smart, then I get an "a"
if its December 25, it is Christmas
ReplyDeleteif its Christmas, its December 25
If it is march 14 then it is pi day
ReplyDeleteif it's pi day it is march 14
If I get a 89.5 percent or higher on my test, I got an A.
ReplyDeleteIf I got an A on on my test, I got a 89.5 percent or higher.
If I get a 89.5 percent or higher on my test, I got an A.
ReplyDeleteIf I got an A on on my test, I got a 89.5 percent or higher.
If I get a 89.5 percent or higher on my test, I got an A.
ReplyDeleteIf I got an A on on my test, I got a 89.5 percent or higher.