Conditional Statements and Equivalence

Question 1

Given the statement "If a line is horizontal, then it has slope equal to zero,” what is its contrapositive?

Revolt · Accepted Answer

If a line does not have zero slope, then it is not a horizontal line.

Question 2

Use the given conditional statement to determine the converse and inverse statements.

Revolt · Accepted Answer

✔ If a line has an undefined slope, then it is a vertical line.; Converse:: If a line has an undefined slope, then it is a vertical line.; Inverse:: If a line is not vertical then it does not have an undefined slope.

Question 3

If a line is vertical then it has an undefined slope.If a line has an undefined slope, then it is a vertical line.✔ If a line is not vertical then it does not have an undefined slope.If a line does not have an undefined slope, then it is not a vertical line.

Revolt · Accepted Answer

✔ If a line is not vertical then it does not have an undefined slope.

Question 4

Given the statement "If there is a lightning storm, then we won’t go swimming,” which is the contrapositive?

Revolt · Accepted Answer

If we go swimming, then there will not be a lightning storm.

Question 5

Based on the diagram, which is a true statement?

Revolt · Accepted Answer

If a student is an honor student, then he/she may also be a band member.

Question 6

Determine the truth value of the given conditional statement.Given: If 3 is an even number, then 5 + 3 = 8.

Revolt · Accepted Answer

A false statement implies a true statement , so the conditional statement is true.

Question 7

Let n be a whole number, and consider the statements below.p: n is a multiple of two.q: n is an even number.Which of the following is equivalent to ~q → ~p?

Revolt · Accepted Answer

p → q

Question 8

Use the given conditional statement to determine the converse and inverse statements.

Revolt · Accepted Answer

The logical statement represents the inverse of the conditional statement “If you are human, then you were born on Earth.”: If you are not human, then you were not born on Earth.; Which statement is the converse?: If you were born on Earth, then you are human.; Are the converse and the inverse true statements? Explain.: No, because there are nonhuman creatures on Earth.

Question 9

✔ If you are not human, then you were not born on Earth.If you are human, then you were born on Earth.If you were not born on Earth, then you are not human.If you were born on Earth, then you are not human.

Revolt · Accepted Answer

✔ If you are not human, then you were not born on Earth.; The logical statement represents the inverse of the conditional statement “If you are human, then you were born on Earth.”: If you are not human, then you were not born on Earth.; Which statement is the converse?: If you were born on Earth, then you are human.; Are the converse and the inverse true statements? Explain.: No, because there are nonhuman creatures on Earth.

Question 10

If you were not born on Earth, then you are not human.✔ If you were born on Earth, then you are human.If you are human, then you were not born on Earth.If you were born on Earth, then you are not human.

Revolt · Accepted Answer

✔ If you were born on Earth, then you are human.

Conditional Statements and Equivalence Answers

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