USC Logic Web

1.1

The gardener did it. Only the gardener had access to the crime scene. Moreover, the crime scene is littered with the gardener’s prints.

The gardener did it. Only the gardener had access to the crime scene. The scene is littered with the gardener’s prints.

1.2

If you had sent me an email, I would have read it. So, you did not send me one. For if I had read it, we would not find ourselves in this situation.

If you had sent me an email, I would have read it. You did not send me an email. If I had read your email, we would not find ourselves in this situation.

1.3

If I put sugar in my coffee, it will taste fine. But if I put motor oil, it will not taste fine. So, if I put motor oil, I will not put sugar in it.

If I put sugar in my coffee, it will taste fine. If I put motor oil, it will not taste fine. If I put motor oil, I will not put sugar in it.

1.4

The statue is not the same thing as the clay. For the statue only came into being this morning when we molded the clay into one. However, the clay existed before this morning.

The statue is not the same thing as the clay. The statue only came into being this morning. The clay existed even before this morning.

1.5

If the animal in the pen is a zebra, then it is not a cleverly painted mule. But if it is a cleverly painted mule, then a prank is being pulled on us. So, the animal in the pen is not a zebra. For a prank is being pulled on us.

If the animal is a zebra, it is not a mule. If it is a mule, a prank is being pulled on us. The animal in the pen is not a zebra. A prank is being pulled on us.

2.1

If today is Tuesday, then tomorrow is Wednesday. Today is Tuesday. Therefore, tomorrow is Wednesday.

Yes No

2.2

If I win the lottery, then I will feel great. I will feel great. Therefore, I will win the lottery.

Yes No

2.3

If LA is in California, then it is closer to San Diego than to New York. LA is closer to San Diego than to New York. Therefore, LA is in California.

Yes No

2.4

LA is in the west coast or LA is in the east coast. If LA is in the east coast, then it is close to New York. Therefore, LA is close to New York.

Yes No

2.5

Lisa is at home or Lisa is at work. If she is at home, she will be back in a minute. So, she will be back in a minute.

Yes No

2.6

The substance will turn brown or it will turn green. Therefore, the substance will turn green.

Yes No

2.7

The laptop will start if, and only if, it is fully charged. The laptop will start. Therefore, the laptop is fully charged.

Yes No

2.8

Mark Twain wrote Huckleberry Finn if, and only if, Samuel Clemens did. Mark Twain wrote Huckleberry Finn. Therefore, Samuel Clemens did not write Huckleberry Finn.

Yes No

2.9

LA is north of San Francisco if, and only if, LA is south of San Diego. LA is north of San Francisco. Therefore, LA is not south of San Diego.

Yes No

2.10

The tank will be empty unless you filled it. You did not fill the tank. Therefore, the tank will be empty.

Yes No

2.11

You will not win the lottery unless you play. You do not play the lottery. Therefore, you will not win the lottery.

Yes No

2.13

I will buy that car only if it is an Audi. I will not buy that car. Therefore, it is an Audi.

Yes No

2.14

The square root of 2 is rational only if it is a fraction of two integers. The square root of 2 is not rational. Therefore, the square root of 2 is not a fraction of two integers.

Yes No

2.15

USC is located in San Diego only if it is located in California. USC is not located in San Diego. Therefore, USC is not located in California.

Yes No

3.1

Whales live underwater. Few mammals live underwater. Therefore, whales are not mammals.

Valid Invalid

3.2

If today is Monday, then tomorrow is Tuesday. Tomorrow is not Tuesday. Therefore, today is not Monday.

Valid Invalid

3.3

It will either rain today or tomorrow. It will not rain today. So, it will rain tomorrow.

Valid Invalid

3.4

The car will not start unless you turn the ignition. There is no gas in the tank. Therefore, the car will not start.

Valid Invalid

3.5

Every number has a successor. 17 is a number. Therefore, 17 has a successor.

Valid Invalid

4.1

Select all true statements.

An argument may have more than one conclusion. Arguments are made of declarative sentences. An argument may have more than one premise. Some arguments are neither valid nor invalid.

4.2

Select all true statements.

Valid arguments have false conclusions. Valid arguments have true conclusions. A valid argument may have a true or a false conclusion.

4.3

Select all true statements.

Invalid arguments have false conclusions. Invalid arguments with true premises have a false conclusion. A valid argument may have true premises and a true conclusion. Valid arguments with a false conclusion have at least one false premise.

4.4

Select all true statements.

Sound arguments have true conclusions. Sound arguments have true premises. Unsound arguments have false premises. Unsound arguments have a false conclusion.

4.5

Select all true statements.

A valid argument may have true premises and a false conclusion. A valid argument may have false premises and a false conclusion. A sound argument may have true premises and a false conclusion. A sound argument may have true premises and a true conclusion.

Arguments

Argument Form

Validity

Soundness