Biconditional Statements and Logical Reasoning

Draw a conclusion from the statement.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.

• Then it's not odd.
• Then it's a whole number.
• Then its square is divisible by 4
• Then it's even.

Given, "If angles are congruent, then the measures of the angles are equal." Identify the hypothesis.

• If angles are congruent.
• Angles are congruent.
• Then the measures of the angles are equal.
• The measures of the angles are equal.

Conditional: If Maria gets married, then the reception will be at the country club.
What is this statement: If the reception is at the country club, then Maria will be getting married.

• Converse
• Inverse
• Contrapositive
• Negation

Given, "If I have a Siberian Husky, then I have a dog." Identify the conclusion.

• If I have a Siberian Husky.
• I have a Siberian Husky.
• Then I have a dog.
• I have a dog.

Determine whether the stated conclusion is valid.
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments.
R is the midpoint of QS.
Conclusion: QR=RS

• Valid
• R is the midpoint
• Invalid
• A point is the midpoint of a segment.

If the sun is shining it is a beautiful day. If it is a beautiful day then we will go go hiking.

• If the sun is not shining, we will not go hiking.

• If the sun is shining then we will go hiking.

• No conclusion can be made.

• If we go hiking, then it is a beautiful day.

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse.

• If I do not have a Siberian Husky, then I do not have a dog.
• If I have a dog, then I have a Siberian Husky.
• If I do not have a dog, then I do not have a Siberian Husky.
• If I do not have a Siberian Husky, then I have a dog. 

Given, "If I have a Siberian Husky, then I have a dog." Identify the hypothesis.

• If I have a Siberian Husky.
• I have a Siberian Husky.
• Then I have a dog.
• I have a dog.

Draw a conclusion from the statement.
If you are at least 25 year old, then you can rent a car.
You can rent a car

• You are at least 25 years old
• You can rent a car
• You can go on a road trip
• Invalid

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• None