Question 1

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

Accepted Answer

inverse

Answer

contrapositive

Answer

converse

Answer

conditional

Question 2

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

Accepted Answer

−q → −p

Answer

−p → −q

Answer

p → q

Answer

q → p

Question 3

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

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

Answer

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

Answer

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

Answer

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

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

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

Answer

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

Answer

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

Answer

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

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

Answer

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

Answer

If x is not positive, then x is zero.

Answer

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

Question 7

7. What is the contrapositive of the given statement “If x is greater than zero, then x is positive.

Accepted Answer

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

Answer

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

Answer

If x is not positive, then x is zero.

Answer

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

Question 8

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

9. What is the negation of the inverse of the given statement“ If ∆ABC is a right triangle, then itsvtwo sides are perpendicular".

Accepted Answer

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

Answer