Asynchronous Activity 04232024

Which of the following best describes the inverse of a conditional statement?

• If it is in the form of “If p, then q”.

• Both the hypothesis and conclusion are negated.

• The hypothesis and the conclusion are interchanged.

• The hypothesis and the conclusion of its converse are negated.

Answer explanation

The inverse of a conditional statement involves negating both the hypothesis and the conclusion, which is the correct choice in this scenario.

Which of the following forms is a contrapositive of “If p, then q”?

• If p, then q

• If p, then p

• If not p, then not q

• If not q, then not p

Answer explanation

The contrapositive of 'If p, then q' is 'If not q, then not p'. This choice correctly reverses and negates the original statement.

Which of the following forms is an inverse of “If p, then q”?

• If p, then q

• If q, then p

• If not p, then not q

• If not q, then not p

Answer explanation

The correct inverse of 'If p, then q' is 'If not p, then not q' by negating both the antecedent and consequent.

Given the conditional statement “If 𝟐𝒙 + 𝟓 = 𝟕, then 𝒙 = 𝟏”. The statement “If 𝑥 = 1, then 2𝑥 + 5 = 7” is its___________.

• contrapositive

• converse

• hypothesis

• inverse

Answer explanation

The correct choice is 'converse' because the converse of a conditional statement switches the hypothesis and conclusion.

“If the figure is a quadrilateral, then it is a four-sided polygon”.

If a polygon is four-sided, then it is a quadrilateral.

• contrapositive

• converse

• hypothesis

• inverse

Answer explanation

The correct choice is 'converse' because it represents the statement in reverse order, which is equivalent to the original statement.

“If the figure is a quadrilateral, then it is a four-sided polygon”.

If a polygon is not a quadrilateral, then it is not four-sided.

• conclusion

• contrapositive

• converse

• inverse

Answer explanation

The correct choice is 'inverse' because it is the negation of the original conditional statement, switching the hypothesis and conclusion.

“If the figure is a quadrilateral, then it is a four-sided polygon”.

If a polygon is not four-sided, then it is not a quadrilateral.

• contrapositive

• converse

• hypothesis

• inverse

Answer explanation

The correct choice is 'contrapositive' because it is the logically equivalent statement to the given conditional statement.

“If a number is divisible by 2 and 3, then it is divisible by 6”

How is it written in an inverse form?

• If a number is divisible by 6, then it is divisible by 2 and 3.

• If a number is not divisible by 2 and 3, then it is divisible by 6.

• If a number is not divisible by 2 and 3 then it is not divisible by 6.

• If a number is not divisible by 6, then it is not divisible by 2 and 3.

Answer explanation

The correct choice is 'If a number is not divisible by 2 and 3 then it is not divisible by 6.' This is the inverse form of the given statement.

“If a number is divisible by 2 and 3, then it is divisible by 6”

Which of the following is the converse of the statement?

• If a number is divisible by 6, then it is divisible by 2 and 3.

• If a number is not divisible by 2 and 3, then it is divisible by 6.

• If a number is not divisible by 2 and 3 then it is not divisible by 6.

• If a number is not divisible by 6, then it is not divisible by 2 and 3.

Answer explanation

The correct choice is: If a number is divisible by 6, then it is divisible by 2 and 3.

“If a number is divisible by 2 and 3, then it is divisible by 6”

What is its contrapositive?

• If a number is divisible by 6, then it is divisible by 2 and 3.

• If a number is not divisible by 2 and 3, then it is divisible by 6.

• If a number is not divisible by 2 and 3 then it is not divisible by 6.

• If a number is not divisible by 6, then it is not divisible by 2 and 3.

Answer explanation

The contrapositive of the statement is that if a number is not divisible by 6, then it is not divisible by 2 and 3.