Conditional Statements and Equivalence

Question 1

If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ?

Revolt · Accepted Answer

C: the converse of the original conditional statement

Question 2

Given:p: x – 5 =10q: 4x + 1 = 61Which is the inverse of p → q?

Question 3

Which pairs of statements are logically equivalent? Select two options.the inverse and the contrapositive of the original conditional statementthe original conditional statement and its contrapositivethe original conditional statement and its inversethe converse and the inverse of the original conditional statementthe converse and the contrapositive of the original conditional statement

Revolt · Accepted Answer

B: the original conditional statement and its contrapositive; D: the converse and the inverse of the original conditional statement

Question 4

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

Revolt · Accepted Answer

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

Question 5

If an original conditional statement is represented by p → q, which represents the contrapositive?

Revolt · Accepted Answer

B: ~q → ~p

Question 6

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

Revolt · Accepted Answer

D: ~q → p

Question 7

The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.”What is the contrapositive of the original conditional statement?

Revolt · Accepted Answer

C: If a number has a negative cube root, then the number is negative.

Question 8

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

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

Question 9

The statement p → q represents "If a number is doubled, the result is even.”Which represents the inverse?

Revolt · Accepted Answer

A: ~p → ~q where p = a number is doubled and q = the result is even

Question 10

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

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

Conditional Statements and Equivalence Answers

More from this Course

TRY EDGENUITY HACKS