Answers1206310 Geometry Sem 1 - CarlisleMeasuring Length and Angles

Conditional Statements and Equivalence Answers

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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.
2
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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
3

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.
4

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
5

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
6

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

A
~p → ~q
B
~q → ~p
C
q → p
D
p → ~q
7

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

A
p → ~q
B
~p → ~q
C
~q → ~p
D
~q → p
8

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.
9

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.
10

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

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