However, if you are taking the Fundamental Information Technology Engineer Examination or are thinking about choosing Python for the afternoon questions, you will be asked a set story in the field of basic theory, so please take a look.

Venn diagram in the set

First, to explain set theory, let's enter the following code into the ** Python console ** to create a set.

>>> A = {2, 4, 5, 6}
>>> B = {1, 2, 3, 4, 7}
>>> A
{2, 4, 5, 6}
>>> B
{1, 2, 3, 4, 7}

I created two sets this time, but the figures are as follows. This diagram is called a ** Venn diagram **.

As you can see from this Venn diagram, ** {2, 4} ** are common to each set in ** A ** and ** B **, respectively. Therefore, the Venn diagram can be expressed as follows.

Theory in sets

Since there are many theoretical stories here, I will explain using the general expression "set" instead of the expression "set".

A ** set ** is a set that is gathered under certain ** conditions **. In the above example, a set of numerical values was created, but for example, set X "people with hair length less than 1 cm" and set Y "people with height 170 cm or more" are ** conditions **.

For example, "a person with short hair" and "a person with high height" depends on the subjectivity of the person, so this is not a condition. Specifically, think of the condition as being expressed numerically.

Set arithmetic

Here, we will introduce the operations in sets.

Union

It is the sum of two sets. In the example of the set ** A ** and the set ** B ** above, the ones contained in either one or more sets ** are output. (Sometimes called ** OR operation **.) It is expressed by one of the following notations.

A∪B, 　A+B, 　A∨B, 　A　or　B

Therefore, it can be expressed as follows.

A∪B = \{1, 2, 3, 4, 5, 6, 7\}

In the Venn diagram, the following colors are applied.

When implemented in Python, it will be as follows. (Use the ** | ** (bar) at the "\ symbol" on the keyboard.)

>>> A | B
{1, 2, 3, 4, 5, 6, 7}

Alternatively, you can also use the ** union method **.

>>> A.union(B)
{1, 2, 3, 4, 5, 6, 7}

Intersection

It is the product of two sets. In the example of the set ** A ** and the set ** B ** above, the ones contained in both ** sets ** are output. (Sometimes called ** AND operation **.) It is expressed by one of the following notations.

A∩B,A / B, 　A∧B, 　A　and　B

Therefore, it can be expressed as follows.

A∩B = \{2, 4\}

In the Venn diagram, the following colors are applied.

When implemented in Python, it will be as follows.

>>> A & B
{2, 4}

Alternatively, you can also use the ** intersection method **.

>>> A.intersection(B)
{2, 4}

Difference set

It is one set minus the elements of another set. In the example of the set ** A ** and the set ** B ** above, the ** items that are included in the set A but not in the set B are output. It is expressed by the following notation method.

A-B

Therefore, it can be expressed as follows.

A-B = \{5, 6\}

In the Venn diagram, the following colors are applied.

When implemented in Python, it will be as follows.

>>> A - B
{5, 6}

Alternatively, it can be calculated using the ** difference method **.

>>> A.difference(B)
{5, 6}

Symmetric set

It's a bit difficult to express, but the output is the one that meets either condition minus the one that meets both conditions (sometimes called ** XOR operation **). What this means is that A-B and B-A are performed on the difference set, and each is ORed. It is expressed by the following notation method.

A⊕B, 　A　xor　B

Therefore, it can be expressed as follows.

A⊕B = \{1, 3, 5, 6, 7\}

In the Venn diagram, the following colors are applied.

When implemented in Python, it will be as follows.

>>> A ^ B
{1, 3, 5, 6, 7}

Alternatively, it can be calculated using the ** symmetric_difference method **.

>>> A.symmetric_difference(B)
{1, 3, 5, 6, 7}

Complement

It means the negation of a set. It means that it is not included in the set ** A **. (Sometimes called ** NOT operation **.) Note that the complement cannot be implemented in Python. It is expressed by the following notation method.

\overline{A},　not A

Therefore, it can be expressed as follows.

\overline{A} = {1, 3, 7}

In the Venn diagram, the following colors are applied. * </ font> The complement covers the part other than the set ** A **. Therefore, the set ** B ** is also a range, and the outer part is also a range.

>>> P = {1, 2, 3, 4, 5, 6, 7}
>>> Q = {3, 5}
>>> P
{1, 2, 3, 4, 5, 6, 7}
>>> Q
{3, 5}

>>> P & Q
{3, 5}

Q⊂P,　Q⊆P

>>> P
{1, 2, 3, 4, 5, 6, 7}
>>> Q
{3, 5}
>>> A
{2, 4, 5, 6}
>>> Q <= P
True
>>> Q <= A
False

>>> Q.issubset(P)
True