Consider the set $A$ of all triads $(a,b,c)$ such that $a+b>c$, $c+a>b$, $b+c>a$. Let the set of all triangles be $T$. Two elements of $T$ will be said to be the same if both of them are having the same sides. Does there exists a one-one correspondence between the sets $A$ and $T$?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
You may need to adjust this. $A$ will contain $(2,3,4)$, $(2,4,3)$, $(3,2,4)$, $(3,4,2)$ $(4,2,3)$ and $(4,3,2)$ as distinct elements but the definition of $T$ might treat these as the same.
Another issue to check is showing each side is positive, though for $a$ this follows from $a + b \gt c$ and $c + a \gt b$ and similarly for the other two.