Conditional Statements and Equivalence

Question 1

Which statement represents a true conclusion, based on the Venn diagram?

Revolt · Accepted Answer

C: Some numbers that are multiples of three are also even numbers.

Question 2

Given the statement "If Jack’s pet is a pig, then Jack’s pet cannot fly,” which statement represents the converse?

Revolt · Accepted Answer

A: q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly

Question 3

Given:p: student achieves 90 percent on the geometry final.q: student will receive a passing grade in geometry class.Which statement is logically equivalent to q → p?

Revolt · Accepted Answer

C: If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class.

Question 4

Which is the contrapositive of p → q?

Revolt · Accepted Answer

D: If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.

Question 5

Question 5

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 6

✔ 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

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

Question 7

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

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

Question 8

Yes, because all humans were born on Earth.Yes, because there are nonhuman creatures on Earth.No, because all humans were born on Earth.✔ No, because there are nonhuman creatures on Earth.

Revolt · Accepted Answer

D: ✔ No, because there are nonhuman creatures on Earth.

Conditional Statements and Equivalence Answers

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