Conditional Statements and Equivalence

Question 1

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

Revolt · Accepted Answer

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

Question 2

✔ 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 3

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.

Question 4

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

✔ No, because there are nonhuman creatures on Earth.

Question 5

Let n be an integer in the conditional statement below.If the last digit of n is zero, then n is divisible by five.

Revolt · Accepted Answer

✔ "The last digit of n is zero."; The hypothesis is:: "The last digit of n is zero."; The conclusion is:: "n is divisible by five."; The converse is:: "If n is divisible by five, the the last digit of n is zero."; The contrapositive is:: "If n is not divisble by five, then n does not end in zero."

Question 6

"The last digit of n is zero."✔ "n is divisible by five.""If n""Then n"

Revolt · Accepted Answer

✔ "n is divisible by five."

Question 7

✔ "If n is divisible by five, the the last digit of n is zero.""If the last digit of n is zero, then n is divisible by five.""If the last digit of n is not zero, then n is not divisible by five.""If n is not divisible by five, then the last digit of n is not zero."

Revolt · Accepted Answer

✔ "If n is divisible by five, the the last digit of n is zero."

Question 8

"If n is divisible by five, then it ends in zero.""If the last digit of n is zero, then n is divisble by five.""If the last digit of n is not zero then n is not divisble by five."✔ "If n is not divisble by five, then n does not end in zero."

Revolt · Accepted Answer

✔ "If n is not divisble by five, then n does not end in zero."

Question 9

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

Revolt · Accepted Answer

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

Question 10

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

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

Conditional Statements and Equivalence Answers

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