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

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 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 3

"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 4

✔ "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 5

"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 6

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 7

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 8

Which is the contrapositive of p → q?

Revolt · Accepted Answer

If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.

Question 9

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

Revolt · Accepted Answer

q → ~p

Question 10

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."

Conditional Statements and Equivalence Answers

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