Conditional Statements and Equivalence Answers

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

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

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

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

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

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.

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

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?

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?

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