Recent content by LCharette

Homework Statement Prove the Int<ABC is a convex set. Homework Equations The Attempt at a Solution 1. Int <ABC = H(A,BC) intersect H(C,AB) by the definition of interior. 2. H(A,BC) is convex and H(C,AB) is convex by Half-Plane Axioms I know I need to show the intersection of...

Am I on the right track with this? Conclusions Justifications 1. p Given 2. ~z or ~y All cases 3. ~z Case 1 4. ~x...

The incidence axioms regarding lines, points, and planes. For example, I-1 states that any line contains two points.

Using the five axioms below prove: p→q A1: p→~y A2: ~r→q A3: p→~z A4: x→ q or z A5: r→x or y Do I have to take the contrapositive of some of the axioms to begin this proof?

I need to prove that every line is contained by at least two planes using only the incidence axioms. This is what I have so far... Conclusions Justifications 1. Let l be any line. Given 2. l has at least two...

Do you have any suggestions on how to prove the intersection of two half planes is convex?

Using the five axioms below prove: p→q A1: p→~y A2: ~r→q A3: p→~z A4: x→ q or z A5: r→x or y Do I have to take the contrapositive of some of the axioms to begin this proof?

I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the intersection of two half planes and using the fact that each half plane is convex. I am stuck on where to go from here.