Sets and Venn Diagrams

Question 1

The logical statement represents the inverse of the conditional statement “If you are human, then you were born on Earth.” Which statement is the converse? Are the converse and the inverse true statements? Explain.

Revolt · Accepted Answer

If you are not human, then you were not born on Earth.; Selection 1: If you are not human, then you were not born on Earth.; Selection 2: If you were born on Earth, then you are human.; Selection 3: No, because there are nonhuman creatures on Earth.

Question 2

Question 2

Revolt · Accepted Answer

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

Question 3

Question 3

Revolt · Accepted Answer

No, because there are nonhuman creatures on Earth.

Question 4

Question 4

Revolt · Accepted Answer

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

Question 5

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 6

Let n be an integer in the conditional statement below.If the last digit of n is zero, then n is divisible by five. The hypothesis is: The conclusion is: The converse is: The contrapositive is:

Revolt · Accepted Answer

"The last digit of n is zero."; Selection 1: "The last digit of n is zero."; Selection 2: "n is divisible by five."; Selection 3: "If n is divisible by five, the the last digit of n is zero."; Selection 4: "If n is not divisble by five, then n does not end in zero."

Question 7

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 8

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.

Question 9

Which is the contrapositive of p → q?

Revolt · Accepted Answer

If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.

Question 10

Given the conditional statement: p → ~q Choose the logically equivalent statement.

Revolt · Accepted Answer

q → ~p

Sets and Venn Diagrams Answers

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