Question

Let n ≥ 2 be any natural number and consider n lines in the xy plane....

Let n ≥ 2 be any natural number and consider n lines in the xy plane. A point in the xy plane is called an intersection point if at least two lines pass through it. Use induction to

show that the number of intersection points is at most (n(n-1))/2.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show that, for any positive integer n, n lines ”in general position” (i.e. no two of...
Show that, for any positive integer n, n lines ”in general position” (i.e. no two of them are parallel, no three of them pass through the same point) in the plane R2 divide the plane into exactly n2+n+2 regions. (Hint: Use the fact that an nth line 2 will cut all n − 1 lines, and thereby create n new regions.)
Suppose that in a Hilbert plane, lines m and n are parallel. Let P be a...
Suppose that in a Hilbert plane, lines m and n are parallel. Let P be a point on m, and Q the point on n so that line P Q is perpendicular to n. Is there another point R on m so that the perpendicular line RS to n through R (where S is incident with n) so that segment P Q is congruent to RS? Under what conditions? (Note that you need to provide some further hypotheses to make...
Use strong induction to prove that every natural number n ≥ 2 can be written as...
Use strong induction to prove that every natural number n ≥ 2 can be written as n = 2x + 3y, where x and y are integers greater than or equal to 0. Show the induction step and hypothesis along with any cases
1. Let R be the rectangle in the xy-plane bounded by the lines x = 1,...
1. Let R be the rectangle in the xy-plane bounded by the lines x = 1, x = 4, y = −1, and y = 2. Evaluate Z Z R sin(πx + πy) dA. 2. Let T be the triangle with vertices (0, 0), (0, 2), and (1, 0). Evaluate the integral Z Z T xy^2 dA ZZ means double integral. All x's are variables. Thank you!.
Prove using induction that for any m,n is an element of natural number, if |{1,2,....,m}|= |{1,2,...,n}|...
Prove using induction that for any m,n is an element of natural number, if |{1,2,....,m}|= |{1,2,...,n}| then n=m
How would you prove that for every natural number n, the product of any n odd...
How would you prove that for every natural number n, the product of any n odd numbers is odd, using mathematical induction?
Let A ={1-1/n | n is a natural number} Prove that 0 is a lower bound...
Let A ={1-1/n | n is a natural number} Prove that 0 is a lower bound and 1 is an upper bound:  Start by taking x in A.  Then x = 1-1/n for some natural number n.  Starting from the fact that 0 < 1/n < 1 do some algebra and arithmetic to get to 0 < 1-1/n <1. Prove that lub(A) = 1:  Suppose that r is another upper bound.  Then wts that r<= 1.  Suppose not.  Then r<1.  So 1-r>0....
Let S be a collection of subsets of [n] such that any two subsets in S...
Let S be a collection of subsets of [n] such that any two subsets in S have a non-empty intersection. Show that |S| ≤ 2^(n−1).
Prove the following statement: for any natural number n ∈ N, n 2 + n +...
Prove the following statement: for any natural number n ∈ N, n 2 + n + 3 is odd.
Let P be the plane given by the equation 2x + y − 3z = 2....
Let P be the plane given by the equation 2x + y − 3z = 2. The point Q(1, 2, 3) is not on the plane P, the point R is on the plane P, and the line L1 through Q and R is orthogonal to the plane P. Let W be another point (1, 1, 3). Find parametric equations of the line L2 that passes through points W and R.