Question 1

1. Which of the following statements derived −p → −q from p → q ?

Accepted Answer

C. inverse

Answer

B. converse

Answer

D. contrapositive

Answer

A. conditional

Question 2

2. What is the symbolic representation of the contrapositive of a conditional statement ?

Accepted Answer

D.−q → −p

Answer

A. p → q

Answer

C. q → p

Answer

B. −p → −q

Question 3

3.What is the inverse of the statement “ If a polygon is a triangle, then it has three sides”?

Accepted Answer

B. If a polygon is not a triangle, then the number of its sides is not three.

Answer

C. If the number of sides of a polygon is not three, then it is not a triangle

Answer

D. If a triangle is not a polygon, then it is not a closed plane figure.

Answer

A. If a polygon has three sides, then it is a triangle.

Question 4

4. What is the converse of the statement “ If a polygon is a triangle, then it has three sides”?

Accepted Answer

A. If a polygon has three sides, then it is a triangle.

Answer

D. If a triangle is not a polygon, then it is not a closed plane figure.

Answer

B. If a polygon is not a triangle, then the number of its sides is not three.

Answer

C. If the number of sides of a polygon is not three, then it is not a triangle

Question 5

5. What is the converse of the statement “If a number is divisible by 9, then the sum of its digits is divisible by 9.”?

Accepted Answer

B. If the sum of the digits of a number is divisible by 9, then it is divisible by 9.

Answer

A. If the number is not divisible by 9, then the sum of its digits is not divisible by 9

Answer

D. If the sum of the digits of a number is not divisible by 9, then it is not divisible by 9.

Answer

C. If the number is divisible by 9, then the sum of its digits is not divisible by 9

Question 6

6. What is the inverse of the statement, “If x is greater than zero, then x is positive.

Accepted Answer

A. If x is less than zero, then x is not positive.

Answer

C. If x is negative, then x is less than zero.

Answer

D. If x is not positive, then x is zero.

Answer

B. If x is positive, then x is greater than zero.

Question 7

7. What is the contrapositive of the given statement in #6?

Accepted Answer

C. If x is negative, then x is less than zero.

Answer

A. If x is less than zero, then x is not positive.

Answer

B. If x is positive, then x is greater than zero.

Answer

D. If x is not positive, then x is zero.

Question 8

8. What is the converse of the statement “ If ∆ABC is aright triangle, then its two sides are perpendicular.

Accepted Answer

A. If two sides of ∆ABC are perpendicular, then ∆ABC is a right triangle.

Answer

C. If ∆ABC is not a right triangle, then it has no right angle.

Answer

B. If two sides of ∆ABC are not perpendicular, then it is not a right triangle.

Answer

D. If ∆ABC is not a right triangle, then its two sides are not perpendicular.

Question 9

9. What is the negation of the inverse of the given statement in #8?

Accepted Answer

D. If ∆ABC is a right triangle, then its two sides are perpendicular

Answer