Question 1

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

Accepted Answer

<P>inverse</P>

Answer

contrapositive

Answer

<P>converse </P>

Answer

conditional

Question 2

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

Accepted Answer

−𝑞 → −𝑝

Answer

−𝑝 → −𝑞

Answer

𝑞 → 𝑝

Answer

𝑝 → 𝑞

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

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 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.

Answer

If the number is divisible by 9, then the sum of its digits 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 positive, then x is greater than zero.

Answer

If x is not positive, then x is zero.

Answer

If x is negative, then x is less than 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 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 a right triangle, then its two sides are perpendicular

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.

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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