MathDB
Two Statements

Source: 1999 National High School Mathematics League, Exam One, Problem 4

March 10, 2020

Problem Statement

Statement 1: Line aαa\in\alpha, line bβb\in\beta, and a,ba,b are skew lines. If c=αβc=\alpha\cap\beta, then cc intersects at most one of a,ba,b. Statement 2: It's impossible to find infintely many lines, any two of them are skew lines. (A)\text{(A)} Statement 1 is true, Statement 2 is false. (B)\text{(B)} Statement 2 is true, Statement 1 is false. (C)\text{(C)} Both are true. (D)\text{(D)} Neither is true.