Reasoning

(a)   is a reasoning that uses facts, rules, definitions, or properties in a logical order to show that a desired conclusion is true.

(a)   is to angle as meter is to length

Hypothesis: A pentagon has five vertices

      Conclusion: A pentagon has five sides.

Which of these conditional statements corresponds to the given statements?

• a. If a pentagon has five sides, then it has five vertices.

• b. A pentagon has five sides only if it has five vertices.

• c. A pentagon has five sides whenever it has five vertices.

• d. A triangle has five vertices if it has five sides.

• a. p↔q

Which of the following conditional statements is true?

• a. If two lines have the same length, then they are coincident.

• A polygon is a rhombus whenever it has four vertices.

• Lines meet at a common point if they are concurrent.

• Points are coplanar only if they are collinear

Which of the following conditional statements is false?

• a. If x + 3 = 10, then x = 7.

• b. A polygon has three sides only if it is a triangle.

• c. A figure is a square whenever its four sides are equal.

• d. The number 8 is a prime number if its factors are 8 and 1.

 If 1 + 1 = 0, then 3 x 5 = 15.

Which of the following is the inverse of the conditional statement?

• a. If 3 x 5 = 15, then 1 + 1 = 0.

• b. 1+ 1 = 0 if and only if 3 x 5 = 15.

• c. If 3 x 5  15, then 1 + 1   0.

• d. If 1 + 1  0, then 3 x 5   15.

What is the truth value of the statement: If 1 + 1  0, then 3 x 5   15?

• true

• false

• maybe

• unknown