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

A
~p → ~q
B
~q → ~p
C
q → p
D
p → ~q
3

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
4

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.
5

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
6

Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.

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 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.
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?

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.
9

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
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.

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