Conditional Statements and Equivalence

Question 1

Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.

Question 2

The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”What is the converse of the original statement?

Revolt · Accepted Answer

If an item is worth five dimes, then it is worth two quarters.

Question 3

What is the converse of the conditional statement?If x is even, then x + 1 is odd.

Revolt · Accepted Answer

If x + 1 is odd, then x is even.

Question 4

Given a conditional statement p → q, which statement is logically equivalent?

Revolt · Accepted Answer

~q → ~p

Question 5

What is the contrapositive of the conditional statement?If two variables are directly proportional, then their graph is a linear function.

Revolt · Accepted Answer

If the graph of two variables is not a linear function, then the two variables are not directly proportional.

Question 6

Given:p: 2x = 16q: 3x – 4 = 20Which is the converse of p → q?

Revolt · Accepted Answer

If 3x – 4 = 20, then 2x = 16.

Question 7

Given:p: Two linear functions have different coefficients of x.q: The graphs of two functions intersect at exactly one point. Which statement is logically equivalent to q → p?

Revolt · Accepted Answer

If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect at exactly one point.

Question 8

Given the conditional statement ~p → q, which statement is logically equivalent?

Revolt · Accepted Answer

~q → p

Question 9

Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.

Revolt · Accepted Answer

If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.; If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.; If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.

Question 10

What is the inverse of the statement?A number that has exactly two distinct factors is prime.

Revolt · Accepted Answer

If a number does not have exactly two distinct factors, then the number is not prime.

Conditional Statements and Equivalence Answers

More from this Course

TRY EDGENUITY HACKS