Taking the contrapositive of this statement?

  • Thread starter Thread starter bonfire09
  • Start date Start date
  • Tags Tags
    Contrapositive
bonfire09
Messages
247
Reaction score
0
Statement: If every right triangle has angle defect equal to zero then the angle defect of every triangle is equal to zero

Taking the contrapositive do i have this correct? : There exists at least one triangle whose angle defect is not zero such that not every right triangle has an angle defect equal to zero.
 
Physics news on Phys.org
The contrapositive of a conditional is another conditional. But there appears to be no conditional in your version - instead, you've a 'such that'. 'if' at the front and 'then' for 'such that',
 
R = the set of all right triangles
T = the set set of triangles
Z = the set of all triangles with angle defect zero

If (for all x in R, x is in Z), then (for all x in T, x is in Z).

The contrapositive of ##p\Rightarrow q## is ##\lnot q\Rightarrow\lnot p##, so the contrapositive of the implication above is

If (there exists an x in T such that x is not in Z), then (there exists an x in R such that x is not in Z).
 
Namaste & G'day Postulate: A strongly-knit team wins on average over a less knit one Fundamentals: - Two teams face off with 4 players each - A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest) I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players. Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that...
Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...

Similar threads

Replies
5
Views
2K
Replies
17
Views
2K
Replies
1
Views
1K
Replies
10
Views
2K
Replies
9
Views
3K
Replies
3
Views
2K
Replies
14
Views
1K
Back
Top