7.
Identify the conclusion of the conditional statement.
If you live in Phoenix, then you live in Arizona.
You live in Phoenix.
You live in Arizona.
9 answers
Conclusion: You live in Arizona.
8.
Which of these conditional statements is false, but has a true converse?
If you live in Canada, then you do not live in the United States.
If you live in the United States, then you do not live in Canada.
If you live in Illinois, then you live in the United States.
If you live in the United States, then you live in Illinois.
Which of these conditional statements is false, but has a true converse?
If you live in Canada, then you do not live in the United States.
If you live in the United States, then you do not live in Canada.
If you live in Illinois, then you live in the United States.
If you live in the United States, then you live in Illinois.
The false statement with a true converse is:
If you live in Illinois, then you live in the United States.
The converse of this statement is:
If you live in the United States, then you live in Illinois.
This statement is true, as living in Illinois implies living in the United States.
If you live in Illinois, then you live in the United States.
The converse of this statement is:
If you live in the United States, then you live in Illinois.
This statement is true, as living in Illinois implies living in the United States.
9.
Which is a counterexample that shows the statement is false?
All whole numbers are even.
6
4
9
2
Which is a counterexample that shows the statement is false?
All whole numbers are even.
6
4
9
2
The number 9 is a counterexample that shows the statement "All whole numbers are even" is false, because 9 is a whole number but it is not even.
10.
Which of these true conditional statements has a false converse?
If a number is divisible by 2, then it is even.
If x > 10, then x > 5.
If x = 2, then 2x = 4.
Which of these true conditional statements has a false converse?
If a number is divisible by 2, then it is even.
If x > 10, then x > 5.
If x = 2, then 2x = 4.
The true conditional statement with a false converse is:
If a number is divisible by 2, then it is even.
Its false converse is:
If a number is even, then it is divisible by 2.
This false because being even does not necessarily mean it is divisible by 2 (e.g., -4 is even but not divisible by 2).
If a number is divisible by 2, then it is even.
Its false converse is:
If a number is even, then it is divisible by 2.
This false because being even does not necessarily mean it is divisible by 2 (e.g., -4 is even but not divisible by 2).
Test the conditional statement and its converse to determine whether the following biconditional is true.
x3 = 125 if and only if x = 5.
A.
It is true because at least one part of the biconditional is true.
B.
It is true because both parts of the biconditional are true.
C.
It is false because both parts of the biconditional are false.
D.
It is false because at least one part of the biconditional is false.
x3 = 125 if and only if x = 5.
A.
It is true because at least one part of the biconditional is true.
B.
It is true because both parts of the biconditional are true.
C.
It is false because both parts of the biconditional are false.
D.
It is false because at least one part of the biconditional is false.
To determine if the biconditional "x^3 = 125 if and only if x = 5" is true, we need to test both directions:
1. If x^3 = 125, then x = 5:
When x = 5, 5^3 = 125, so this direction is true.
2. If x = 5, then x^3 = 125:
When x = 5, 5^3 = 125, so this direction is also true.
Since both parts of the biconditional are true, the correct answer is:
B. It is true because both parts of the biconditional are true.
1. If x^3 = 125, then x = 5:
When x = 5, 5^3 = 125, so this direction is true.
2. If x = 5, then x^3 = 125:
When x = 5, 5^3 = 125, so this direction is also true.
Since both parts of the biconditional are true, the correct answer is:
B. It is true because both parts of the biconditional are true.
3 answers