AnswersFL-1206310-Geometry A - FlexConditional Statements and Equivalence

Conditional Statements and Equivalence Answers

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

A
p → ~q
B
~p → ~q
C
~q → ~p
D
~q → p
2
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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

A
the inverse and the contrapositive of the original conditional statement
B
the original conditional statement and its contrapositive
C
the original conditional statement and its inverse
D
the converse and the inverse of the original conditional statement
E
the converse and the contrapositive of the original conditional statement
3

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

A
If two variables are directly proportional, then their graph is not a linear function.
B
If two variables are not directly proportional, then their graph is not a linear function.
C
If the graph of two variables is a linear function, then the two variables are directly proportional.
D
If the graph of two variables is not a linear function, then the two variables are not directly proportional.
4

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?

A
If an item is not worth two quarters, then it is not worth five dimes.
B
If an item is worth two quarters, then it is worth five dimes.
C
If an item is worth five dimes, then it is worth two quarters.
D
If an item is not worth five quarters, then it is worth two dimes.
5

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

A
~p → ~q where p = a number is doubled and q = the result is even
B
q → p where p = a number is doubled and q = the result is even
C
~p → ~q where p = the result is even and q = a number is doubled
D
q → p where p = the result is even and q = a number is doubled
6

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.

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.
C
If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.
D
If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
E
If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
7

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

A
If a number has exactly two distinct factors, then the number is prime.
B
If a number does not have exactly two distinct factors, then the number is not prime.
C
If a number is not prime, then the number does not have exactly two distinct factors.
D
If a number is prime, then the number has exactly two distinct factors.
9

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

A
~p → ~q
B
~q → ~p
C
q → p
D
p → ~q
10

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

A
If x – 5 ≠ 10, then 4x + 1 ≠ 61.
B
If 4x + 1 ≠ 61, then x – 5 ≠ 10.
C
If x – 5 = 10, then 4x + 1 = 61.
D
If 4x + 1 = 61, then x – 5 = 10.
11

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

A
q → p
B
~q → ~p
C
p → q
D
~p → ~q
12

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?

A
If a number is negative, then it does not have a negative cube root.
B
If a number does not have a negative cube root, then the number is not negative.
C
If a number has a negative cube root, then the number is negative.
D
If a number is not negative, then it does not have a negative cube root.
13

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

Question illustration
A
the original conditional statement
B
the inverse of the original conditional statement
C
the converse of the original conditional statement
D
the contrapositive of the original conditional statement
14

Question text not available

Question illustration
A
If a number is prime, it is also odd.
B
If a number is odd, it is also prime.
C
If a number is not odd, it cannot be prime.
D
If a number is prime, it may or may not be odd.
15

Which pairs of statements are logically equivalent? Select two options.

A
the inverse and the contrapositive of the original conditional statement
B
the original conditional statement and its contrapositive
C
the original conditional statement and its inverse
D
the converse and the inverse of the original conditional statement
E
the converse and the contrapositive of the original conditional statement
16

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

A
the original conditional statement
B
the converse of the original conditional statement
C
the contrapositive of the original conditional statement
D
the inverse of the original conditional statement
17

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?

A
If an item is not worth two quarters, then it is not worth five dimes.
B
If an item is worth two quarters, then it is worth five dimes.
C
If an item is worth five dimes, then it is worth two quarters.
D
If an item is not worth five quarters, then it is worth two dimes.
18

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?

A
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one point.
B
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.
C
If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same coefficients of x.
D
If the graphs of two functions intersect at exactly one point, then the two linear functions have the same coefficients of x.
19

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

A
If x is not even, then x + 1 is not odd.
B
If x + 1 is odd, then x is even.
C
If x + 1 is not odd, then x is not even.
D
If x is even, then x + 1 is not odd.
20

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

A
If a number has exactly two distinct factors, then the number is prime.
B
If a number does not have exactly two distinct factors, then the number is not prime.
C
If a number is not prime, then the number does not have exactly two distinct factors.
D
If a number is prime, then the number has exactly two distinct factors.

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