Question 1

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

Accepted Answer

inverse

Answer

converse

Answer

conditional

Answer

contrapositive

Question 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

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 polygon has three sides, then it is a triangle

Answer

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

Question 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

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

Question 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 positive, then x is greater than zero.

Answer

If x is not positive, then x is zero

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

Answer

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

Answer

If x is not positive, then x is zero.

Question 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 two sides of ∆ABC are not perpendicular, then it is not 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.

Question 9

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 10

What is the contrapositive of the inverse of the given statement 𝑝 → 𝑞?

Accepted Answer

−q → −p

Answer

−𝑝 → −𝑞

Answer

q → p

Answer

p → q

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