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Conditional Statements and Equivalence Answers

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

q → p

~q → ~p

p → q

~p → ~q

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

If x is not even, then x + 1 is not odd.

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

If x + 1 is not odd, then x is not even.

If x is even, then x + 1 is not odd.

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

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

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

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

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

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

the original conditional statement

the inverse of the original conditional statement

the converse of the original conditional statement

the contrapositive of the original conditional 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?

If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one point.

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.

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

If the graphs of two functions intersect at exactly one point, then the two linear functions have the same coefficients of x.

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

~p → ~q

~q → ~p

q → p

p → ~q

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?

If an item is not worth two quarters, then it is not worth five dimes.

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

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

If an item is not worth five quarters, then it is worth two dimes.

Question text not available

If a number is prime, it is also odd.

If a number is odd, it is also prime.

If a number is not odd, it cannot be prime.

If a number is prime, it may or may not be odd.

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

p → ~q

~p → ~q

~q → ~p

~q → p

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

If x – 5 ≠ 10, then 4x + 1 ≠ 61.

If 4x + 1 ≠ 61, then x – 5 ≠ 10.

If x – 5 = 10, then 4x + 1 = 61.

If 4x + 1 = 61, then x – 5 = 10.

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Conditional Statements and Equivalence Answers

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