13. What can be concluded given the following statements, using the Law of Syllogism: If I eat candy late a night, I will get a stomach ache. If I get a stomach ache, I will not be able to sleep.
Thinking it through, only one of the following four questions should be answerable with a "yes."
A. If I eat candy late at night, then I will not be able to sleep. (Given the above, would you be able to sleep if you ate candy?)
B. If I get a stomach ache, then I ate candy late at night. (Is there no other way you could have gotten the stomach ache?)
C. If I am not able to sleep, then I ate candy late at night. (Is there no other reason you'd be unable to sleep?)
D. If I am not able to sleep, then I have a stomach ache. (Is there no other reason you'd be unable to sleep?)
14. Determine which conclusion can be drawn from the two statements: If three points lie in a plane, they are coplanar. Points A, B, and C lie in plane D (which I believe implies they all lie in the same plane).
A. Points A, B, and C are collinear.
B. Points A, B, and C are coplanar.
C. Points A, B, and C are noncollinear.
D. No conclusion can be reached.
17. Which of the following is a counter-example of the conjecture that all triangles are scalene?
A. an acute triangle
B. an isosceles triangle
C. an obtuse triangle
D. a right triangle
If you google the definition of each of the above types of triangles, you'll see that one definition cannot fall within the definition of a scalene triangle.