Logic and Reasoning Practice and Tutorial

Understanding sentence logic, or syllogisms is tricky – here are some tips to guide you when answering exam questions:

Logical syllogisms have three key components: the major premise, minor premise, and the conclusion. Practicing logic questions helps you identify these quickly and easily.

There are two terms used in each part, which can be understood through the form ““Some/all A is/are [not] B.”

Each premise has a common term with the conclusion as seen in the example below:

Premise: All birds are animals
Premise: All parrots are birds
Conclusion: All parrots are animals

Here, “animal” is the major term and predicate of the conclusion, “parrot” is the minor term and subject of the conclusion, and “bird” is the middle term.

Clearly, this argument is rock-solid. If ALL birds are animals, AND all parrots are birds, then the conclusion must be true – All parrots must be animals.

To check on this, let’s try a variation:

Some birds are animals. All parrots are birds

All parrots are animals.

Clearly, this is not true. If only ‘some’ birds are animals, then there are some birds which are NOT animals, and we don’t have any information about if the ‘some’ birds which are not animals. Perhaps the some birds that are not animals are parrots and perhaps not.

Here is another example:

This store only sells used textbooks.
My textbook is used.
My textbook came from that store.

This is clearly a not true.  We do not know if the store is the only store in the world that sells textbooks, so clearly the textbook in question could have come from that store or any other store.

There are four possible variations to each “Some/all/no A is/are [not] B,” structure.

All birds are animals.
All parrots are birds.
All parrots are animals.

Clearly a very solid argument – IF all birds are animals AND all parrots are birds, then the conclusion, all parrots are animals MUST be true.

Here is a variation that is NOT true:

Some birds are animals.
All parrots are birds.
All parrots are animals.

Here we don’t know if the ‘some’ birds that are NOT animals includes parrots or not. They may be but we don’t know.

Here is the negative example:

No birds are foxes.
All parrots are birds.
No parrots are foxes.

A very good argument where the conclusion, No parrots are foxes MUST be true if the premises are true.

Notice what happens if we substitute ‘some’ into the argument.

Some birds are foxes.
All parrots are birds.
No parrots are foxes.

No birds are foxes.
Some parrots are birds.
No parrots are foxes.

Both of these are clearly false.   The argument relies on the fact the absolute statements ALL and NONE.

Using ‘some’ can give a very solid argument though.

Consider these:

All dogs are animals.
Some mammals are dogs.
Some mammals are animals.

No dogs are birds.
Some mammals are dogs.
Some mammals are not birds.

No restaurant food is healthy.
Some recipes are healthy.
Some recipes are not restaurant foods.

All liars are evildoers.
Some doctors are not evildoers.
Some doctors are not liars.

All of these are very good arguments where the conclusion MUST be true if the premises are true.

Generally, exam questions are not exactly like the forms we have been discussing so far, but are similar. Understanding the correct forms is still very important and necessary to understanding the underlying structure. Here are some example logic questions:

1. Practice makes perfect.
I am perfect.
I practiced a lot.

If the first 2 statements are true, then the third statement is:

True False Uncertain

The correct answer is – Uncertain. There are all sorts of reasons you could be perfect without practicing.   For example, you could be perfect looking, or your hair could be perfect, or you could be perfect by a coincidence.

2. People who smoke cigarettes have a 75% chance of getting cancer.
I have cancer.
I smoked a lot.

If the first 2 statements are true, then the third statement is:

True False Uncertain

The correct answer is – Uncertain. There are many reasons you could have cancer. In addition, you may be among the 25% of people who smoke and do NOT get cancer.

3. Most car accidents happen in the morning.
I don’t drive in the morning.
I am unlikely to have an accident.

If the first 2 statements are true, then the third statement is:

True False Uncertain

The correct answer is – Uncertain.

4. Halibut are a large fish.
I caught a small fish.
I did not catch a halibut.

If the first 2 statements are true, then the third statement is:

True False Uncertain

The correct answer is – False.  You could have caught a baby halibut.   In order for this to be true, you would have to say,

All halibut are large fish.
I caught a small fish.
I did not catch a halibut.

Here, the first premise is ALL halibut are large, which would include baby halibut, so if the first two premises are true, the third statement MUST be true also.

Here is a different style of question.

1. Angel gets the highest grades in all the subjects in school. She is also the president of the Student Council. Every year she gets the highest award given by the school.

a. Angel is a slow
b. Everybody admires
c. Other children are envious of
d. Angel is at the top of her

Let’s look at the choices.   Option a. is clearly false. Option b, may be true but it also may not be true – no information is given. It is likely that everyone admires her, but we don’t know that for sure. The same with option c.

Probably other students are envious of her, but we don’t know that for sure and no information is given. She could, for example, have rigged the election for Student Council and cheated on all her exams and everyone hates her!

Option d. is correct – This we do now for sure.

2. Students enjoy playing football after school. Sometimes, they play basketball with other kids. On weekends, they play baseball, badminton, or tennis.

a. Students prefer playing indoors.
b. Students enjoy different kinds of sports
c. Students hate playing
d. Playing is a form of exercise

The correct answer is B. The only certain thing is children enjoy different kinds of sports. For option A, no information is given if they are playing indoors or outdoors. Option C. is probably false, but we don’t know. Choice D is true, but not related to the information given. Choice D is designed to confuse.