Conditional Statements and Equivalence

Question 1

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

Revolt · Accepted Answer

~q → p

Question 2

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 3

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 4

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

Revolt · Accepted Answer

~q → ~p

Question 5

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

Revolt · Accepted Answer

~q → ~p

Question 6

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 7

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

the original conditional statement and its contrapositive; the converse and the inverse of the original conditional statement

Question 8

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.

Question 9

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

Revolt · Accepted Answer

If 3x – 4 = 20, then 2x = 16.

Question 10

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

Revolt · Accepted Answer

the converse of the original conditional statement

Conditional Statements and Equivalence Answers

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