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Which is the converse of the conditional statement and is true or false?
If a number is a prime number, then it is divisible by 1 and itself.
(Points : 1)
If a number is not divisible by 1 and itself, then it is a prime number. The converse is false.
If a number is not divisible by 1 and itself, then it is not a prime number. The converse is true.
If a number is not a prime number, then it is not divisible by 1 and itself. The converse is false.
If a number is divisible by 1 and itself, then it is a prime number. The converse is false.
Question 2. 2. Which conditional statement has a converse that is true?
(Points : 1)
If I am at the beach, then I am hot.
If I am at home, then I am in my bedroom.
If I am studying, then I am reading.
If I am playing soccer, then I am exercising.
Question 3. 3. Write the inverse of the conditional statement.
If a number is a perfect square, then it is a composite number.
(Points : 1)
If a number is a composite number, then it is a perfect square.
If a number is a composite number, then it is not a perfect square.
If a number is not a composite number, then it is not a perfect square.
If a number is not a perfect square, then it is not a composite number.
Question 4. 4. Which is the contrapositive of the conditional statement?
If an animal is a deer, then it has four legs.
(Points : 1)
If an animal has four legs, then it is a deer.
If an animal does not have four legs, then it has four legs.
If an animal does not have four legs, then it is not a deer.
If an animal is not a deer, then it is does not have four legs.
Question 5. 5. Which shows the contrapositive of the conditional statement, and if the conditional
statement and the contrapositive are true or false?
If |x| ? 3, then x ? 3.
(Points : 1)
If |x| = 3, then x = 3. The conditional statement and the contrapositive are both true.
If x = 3, then |x| = 3. The conditional statement and the contrapositive are both true.
If x = 3, then |x| = 3. The conditional statement is false and the contrapositive is true.
If x ? 3, then |x| ? 3. The conditional statement and the contrapositive are both false.
1.
What is the correct reason for statement 1 in the proof?
(Points : 1)
Multiplication Property of Equality
Given
Addition Property of Equality
Substitution Property
Question 2. 2. Select the correct reason for the numbered statement.
Statement 2
(Points : 1)
Division Property of Equality
Multiplication Property of Equality
Inverse Property of Multiplication
Identity Property of Multiplication
Question 3. 3.
What is the correct reason for statement 3 in the proof?
(Points : 1)
Identity Property of Addition
Distributive Property
Commutative Property of Addition
Associative Property of Addition
Question 4. 4.
What is the correct reason for statement 6 in the proof?
(Points : 1)
Given
Identity Property of Multiplication
Symmetric Property of Equality
Transitive Property Of Equality
Question 5. 5. Which of the following steps in this proof contains a flaw?
(Points : 1)
step 2 (multiplied by wrong expression)
step 4 (subtracted wrong expression)
step 5 (factored incorrectly)
step 6 (factored difference of two squares incorrectly)
Which is a counterexample that disproves the conjecture?
For all real numbers n, |n| > 0.
(Points : 1)
n = –0.5
n=0
n = 0.5
n=3
Question 2. 2. Choose the counterexample that disproves the conjecture.
If n is a two-digit prime number, then the two digits must be different.
(Points : 1)
n = 22
n = 17
n = 11
n = 10
Question 3. 3.
Which is a counterexample that disproves the conjecture?
A student concludes that if x is a positive real number, then
(Points : 1)
x=0
x = 0.25
x=3
x=1
Question 4. 4. Which is a counterexample that disproves the conjecture?
A student concludes that if x is a real number, then x2 = x4.
(Points : 1)
Question 5. 5. Which is a counterexample that disproves the conjecture?
After completing several multiplication problems, a student concludes that the product of two
binomials is always a trinomial.
(Points : 1)

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