Logical Arguments

Determine whether the stated conclusion is valid.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.

• Invalid
• Valid
• Sammy is a Great Dane
• Sammy is really a cat.

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

Draw a conclusion from the statement.
If you go fishing, then you will need to bring your fishing rod.
You go fishing.

• You will need to bring your fishing rod.
• Invalid
• You are a boring person.
• You are going to catch a fish.

Use the law of syllogism to draw a conclusion from the two given statements:
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy

• You have more energy
• If you exercise regularly, then you have more energy
• You have a healthy body
• If you do not have a healthy body, then you do not exercise regularly

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If I study for one hour each day, then I will score well on the exam
Statement 2: I will score well on the exam

•  I study for 1 hour each day.
• I do not study for 1 hour each day
• If I do well on the exam, I studied for 1 hour each day.
• not possible

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, therefore

• look out for the snowplows while driving to school.
• the big test will not be given today.
• the roads will be hard to drive on.
• you should call the school to see if school is canceled.

If the binding of the book is broken, then the student will have to pay for a new one. Michael has to pay for a new book, so he concludes the binding on his book is broken. Is he correct?

• Yes
• No

(1) If you have a can opener, you can open a can.
(2) Jon has a can opener.
(3) John can open a can.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Syllogism
• Law of Detachment
• invalid

If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?

• ∠A is complementary to ∠B
• ∠A is acute.
• ∠A is obtuse.
• ∠A is 40⁰

(1)  If it is a rabbit, then it has long ears.
(2)  Peter Cottontail has long ears.
(3)  Peter Cottontail is a rabbit.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• invalid