Question

1.Select the conclusion of the conditional statement.

If you make an omelet, then you will need two eggs

2.Use the conditional statement to answer the question.
If an animal is an insect, then the animal has six legs.
What is the contrapositive of the statement?
A)If an animal is an insect, then the animal does not have six legs.
B)If an animal has six legs, then the animal is an insect.
C)If an animal is not an insect, then the animal does not have six legs.
D)If an animal does not have six legs, then the animal is not an insect.

3.Use the conditional statement to answer the question.
If an angle is a right angle, then the angle measures 90°.
Are the statement and its contrapositive true?
A)The statement is true, but the contrapositive is false.
B)The statement is false, but the contrapositive is true.
C)Both the statement and its contrapositive are true.
D)Both the statement and its contrapositive are false.

4.Use the conditional statement to answer the question.
If today is Monday, then yesterday was Sunday.
Can the statement be written as a biconditional statement and why?
A)Yes, because the statement and its converse are both true
B)No, because the statement is false, but its converse is true
C)No, because the statement is true, but its converse is false
D)No, because the statement and its converse are both false

Is each biconditional statement true or false?
Select True or False for each statement.

True False
A number is a multiple of 3 if and only if the number is odd.
A number is even if and only if the number is divisible by 2.
A number is prime if and only if the number is not a multiple of 4.

Answer 1

The conclusion is: You will need two eggs

Part 2; Option D: If an animal does not have six legs, then the animal is not an insect"

Part 3; Option C: Both the statement and its contrapositive are true

Part 4; Option A: Yes, because the statement and its converse are both true

Part 5;

A: False

B: True

C: False

Answer 2

Part 1) The conclusion is "you will need two eggs"

Part 2) Option D "If an animal does not have six legs, then the animal is not an insect"

Part 3) Option C Both the statement and its contrapositive are true

Part 4) Option A Yes, because the statement and its converse are both true

Part 5) a) False b) True c) False

Explanation:

Part 1) we know that

A conditional statement is a statement that can be written of the form "if p then q"

p ----> q

where

The hypothesis is the "p" part of the conditional statement following the word "if"

The conclusion is the "q" part of the conditional statement following the word "then"

In this problem we have

"If you make an omelet, then you will need two eggs"

therefore

The hypothesis is "you make an omelet"

The conclusion is "you will need two eggs"

Part 2) we have

"If an animal is an insect, then the animal has six legs"

we know that

The contrapositive is the statement formed by both exchanging and negating the hypothesis and conclusion

The hypothesis is "an animal is an insect"

The conclusion is "the animal has six legs"

exchanging and negating the hypothesis and conclusion

The hypothesis is "an animal does not have six legs"

The conclusion is "the animal is not an insect"

therefore

The contrapositive is

"If an animal does not have six legs, then the animal is not an insect"

Part 3) we have

"If an angle is a right angle, then the angle measures 90°"

Are the statement and its contrapositive true?

we know that

The measure of a right angle measures 9 degrees

so

The statement is true

The contrapositive (statement formed by both exchanging and negating the hypothesis and conclusion) is equal to

"If an angle not measures 90°, then the angle is not a right angle"

The contrapositive is true

therefore

Both the statement and its contrapositive are true

Part 4) Use the conditional statement to answer the question.

"If today is Monday, then yesterday was Sunday"

Can the statement be written as a biconditional statement and why?

we know that

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form

A biconditional is true if and only if both the conditionals are true

The converse is the statement formed by exchanging the hypothesis and conclusion

we have

The conditional statement is

"If today is Monday, then yesterday was Sunday"

The hypothesis is "today is Monday"

The conclusion is "yesterday was Sunday"

Find out the converse (exchanging the hypothesis and conclusion)

The hypothesis is "yesterday was Sunday"

The conclusion is "today is Monday"

The converse is

"If yesterday was Sunday, then today is Monday"

Both the statement and its converse are true

therefore

The statement can be written as a biconditional statement, because the statement and its converse are both true

Part 5) Is each biconditional statement true or false?

case a) A number is a multiple of 3 if and only if the number is odd

Is False, because 6 is a multiple of 3 but 6 is not an odd number

case b) A number is even if and only if the number is divisible by 2

Is True, all even numbers are multiple of 2, therefore the given biconditional statement in true

case c) A number is prime if and only if the number is not a multiple of 4

Is False, because 6 is not a multiple of 4 but 6 is not a prime number