1. ## 3 math questions. please solve

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.

A. If I eat candy late at night, then I will not be able to sleep.
B. If I get a stomach ache, then I ate candy late at night.
C. If I am not able to sleep, then I ate candy late at night.
D. If I am not able to sleep, then I have a stomach ache.

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.

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

2. ## 3 math questions. please solve

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.

Steve J

3. dgenerationx2!

You seem to be lacking most of the basic knowledge of Logic.
Have you been ill for an extended period?

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.

A. If I eat candy late at night, then I will not be able to sleep.
B. If I get a stomach ache, then I ate candy late at night.
C. If I am not able to sleep, then I ate candy late at night.
D. If I am not able to sleep, then I have a stomach ache.

Evidently, you don't know the Law of Syllogism . . .

. . It says: .$\displaystyle \begin{array}{c}p \to q \\ q \to r \\ \hline p \to r \end{array}$

$\displaystyle \text{We are given: }\;\begin{array}{ccc}\underbrace{\text{eat candy}}_{p} &\to & \underbrace{\text{stomach ache}}_{q} \\ \\[-3mm] \underbrace{\text{stomach ache}}_q & \to & \underbrace{\text{not sleep}}_{r} \\ \\[-3mm] \hline \end{array}$

$\displaystyle \text{Therefore: }\qquad\quad \begin{array}{ccc}\underbrace{\text{eat candy}}_p &\to& \underbrace{\text{not sleep}}_r \end{array}$

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.

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.
Nor do you know the Law of Detachment:

. . . $\displaystyle \begin{array}{c}p \to q \\ p\qquad \\ \hline q\qquad \end{array}$

$\displaystyle \text{We are given: }\;\begin{array}{c}\underbrace{\text{A, B, C are in a plane}}_p \;\to\;\underbrace{\text{A, B, C are coplanar}}_q \\ \\[-3mm] \underbrace{\text{A, B, C are in a plane}}_q\qquad\qquad\qquad\qquad\qquad\quad \\ \\[-3mm] \hline\end{array}$

$\displaystyle \text{Therefore: }\qquad \underbrace{\text{A, B, C are coplanar} }_q$

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

Do you even know what a scalene triangle is?