QuestionEstudia los gustos cinematográficos de estudiantes y calcula:
a.) $A \cap P$ : b.) $C \cup S$ : c.) $C^{\prime} \cup S^{\prime}$ d.) $(A \cap P)^{\prime}$

Studdy Solution

STEP 1

Assumptions1. The table represents the distribution of students' movie preferences and their grade levels. . The intersection ( $\cap$ ) represents students who belong to both categories.
3. The union ( $\cup$ ) represents students who belong to either or both categories.
4. The complement ( $'$ ) represents students who do not belong to the category.

STEP 2

To find the number of students in the set $A \cap$ , we look at the intersection of the row "Aventura A" and the column "Primero" in the table.

STEP 3

From the table, we see that the number of students who like Adventure movies and are in the first grade is90.
So, $A \cap =90$ .

STEP 4

To find the number of students in the set $C \cup$ , we add the total number of students who like Comedy movies and the total number of students in the second grade. However, since we are counting the students who like Comedy and are in the second grade twice, we need to subtract this intersection once.

STEP 5

From the table, we see that the total number of students who like Comedy movies is231, the total number of students in the second grade is215, and the number of students who like Comedy movies and are in the second grade is76.
So, $C \cup =231 +215 -76$ .

STEP 6

Calculate the number of students in the set $C \cup$ .
$C \cup =231 +215 -76 =370$ .

STEP 7

To find the number of students in the set $C^{\prime} \cup^{\prime}$ , we first need to find the number of students who do not like Comedy movies and the number of students who are not in the second grade. Then, we add these two numbers together. However, since we are counting the students who do not like Comedy and are not in the second grade twice, we need to subtract this intersection once.

STEP 8

From the table, we see that the total number of students is640, the total number of students who like Comedy movies is231, and the total number of students in the second grade is215.
So, the number of students who do not like Comedy movies is $640 -231 =409$ , and the number of students who are not in the second grade is $640 -215 =425$ .

STEP 9

To find the number of students who do not like Comedy and are not in the second grade, we subtract the number of students who like Comedy or are in the second grade from the total number of students.
From the table, we see that the number of students who like Comedy or are in the second grade is $C \cup =370$ .
So, the number of students who do not like Comedy and are not in the second grade is $640 -370 =270$ .

STEP 10

Now, we can calculate the number of students in the set $C^{\prime} \cup^{\prime}$ .
$C^{\prime} \cup^{\prime} =409 +425 -270$ .

STEP 11

Calculate the number of students in the set $C^{\prime} \cup^{\prime}$ .
$C^{\prime} \cup^{\prime} =409 +425 -270 =564$ .

STEP 12

To find the number of students in the set $(A \cap)^{\prime}$ , we first need to find the number of students who like Adventure movies and are in the first grade. Then, we subtract this number from the total number of students.

STEP 13

From the table, we see that the total number of students is640 and the number of students who like Adventure movies and are in the first grade is90.
So, $(A \cap)^{\prime} =640 -90$ .

STEP 14

Calculate the number of students in the set $(A \cap)^{\prime}$ .
$(A \cap)^{\prime} =640 -90 =550$ .
The number of students in each set isa.) $A \cap =90$ b.) $C \cup =370$ c.) $C^{\prime} \cup^{\prime} =564$ d.) $(A \cap)^{\prime} =550$

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QuestionEstudia los gustos cinematográficos de estudiantes y calcula:
a.) $A \cap P$ : b.) $C \cup S$ : c.) $C^{\prime} \cup S^{\prime}$ d.) $(A \cap P)^{\prime}$

Studdy Solution

STEP 1

STEP 2

To find the number of students in the set $A \cap$ , we look at the intersection of the row "Aventura A" and the column "Primero" in the table.

STEP 3

From the table, we see that the number of students who like Adventure movies and are in the first grade is90.
So, $A \cap =90$ .

STEP 4

STEP 5

From the table, we see that the total number of students who like Comedy movies is231, the total number of students in the second grade is215, and the number of students who like Comedy movies and are in the second grade is76.
So, $C \cup =231 +215 -76$ .

STEP 6

Calculate the number of students in the set $C \cup$ .
$C \cup =231 +215 -76 =370$ .

STEP 7

STEP 8

STEP 9

STEP 10

Now, we can calculate the number of students in the set $C^{\prime} \cup^{\prime}$ .
$C^{\prime} \cup^{\prime} =409 +425 -270$ .

STEP 11

Calculate the number of students in the set $C^{\prime} \cup^{\prime}$ .
$C^{\prime} \cup^{\prime} =409 +425 -270 =564$ .

STEP 12

To find the number of students in the set $(A \cap)^{\prime}$ , we first need to find the number of students who like Adventure movies and are in the first grade. Then, we subtract this number from the total number of students.

STEP 13

From the table, we see that the total number of students is640 and the number of students who like Adventure movies and are in the first grade is90.
So, $(A \cap)^{\prime} =640 -90$ .

STEP 14

Calculate the number of students in the set $(A \cap)^{\prime}$ .
$(A \cap)^{\prime} =640 -90 =550$ .
The number of students in each set isa.) $A \cap =90$ b.) $C \cup =370$ c.) $C^{\prime} \cup^{\prime} =564$ d.) $(A \cap)^{\prime} =550$

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QuestionEstudia los gustos cinematográficos de estudiantes y calcula:a.) A∩PA \cap PA∩P : b.) C∪SC \cup SC∪S : c.) C′∪S′C^{\prime} \cup S^{\prime}C′∪S′ d.) (A∩P)′(A \cap P)^{\prime}(A∩P)′

Studdy Solution

STEP 1

STEP 2

To find the number of students in the set A∩A \capA∩, we look at the intersection of the row "Aventura A" and the column "Primero" in the table.

STEP 3

From the table, we see that the number of students who like Adventure movies and are in the first grade is90.So, A∩=90A \cap =90A∩=90.

STEP 4

STEP 5

From the table, we see that the total number of students who like Comedy movies is231, the total number of students in the second grade is215, and the number of students who like Comedy movies and are in the second grade is76.So, C∪=231+215−76C \cup =231 +215 -76C∪=231+215−76.

STEP 6

Calculate the number of students in the set C∪C \cupC∪.C∪=231+215−76=370C \cup =231 +215 -76 =370C∪=231+215−76=370.

STEP 7

STEP 8

STEP 9

STEP 10

Now, we can calculate the number of students in the set C′∪′C^{\prime} \cup^{\prime}C′∪′.C′∪′=409+425−270C^{\prime} \cup^{\prime} =409 +425 -270C′∪′=409+425−270.

STEP 11

Calculate the number of students in the set C′∪′C^{\prime} \cup^{\prime}C′∪′.C′∪′=409+425−270=564C^{\prime} \cup^{\prime} =409 +425 -270 =564C′∪′=409+425−270=564.

STEP 12

To find the number of students in the set (A∩)′(A \cap)^{\prime}(A∩)′, we first need to find the number of students who like Adventure movies and are in the first grade. Then, we subtract this number from the total number of students.

STEP 13

From the table, we see that the total number of students is640 and the number of students who like Adventure movies and are in the first grade is90.So, (A∩)′=640−90(A \cap)^{\prime} =640 -90(A∩)′=640−90.

STEP 14

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QuestionEstudia los gustos cinematográficos de estudiantes y calcula:
a.) $A \cap P$ : b.) $C \cup S$ : c.) $C^{\prime} \cup S^{\prime}$ d.) $(A \cap P)^{\prime}$

To find the number of students in the set $A \cap$ , we look at the intersection of the row "Aventura A" and the column "Primero" in the table.

From the table, we see that the number of students who like Adventure movies and are in the first grade is90.
So, $A \cap =90$ .

From the table, we see that the total number of students who like Comedy movies is231, the total number of students in the second grade is215, and the number of students who like Comedy movies and are in the second grade is76.
So, $C \cup =231 +215 -76$ .

Calculate the number of students in the set $C \cup$ .
$C \cup =231 +215 -76 =370$ .

Now, we can calculate the number of students in the set $C^{\prime} \cup^{\prime}$ .
$C^{\prime} \cup^{\prime} =409 +425 -270$ .

Calculate the number of students in the set $C^{\prime} \cup^{\prime}$ .
$C^{\prime} \cup^{\prime} =409 +425 -270 =564$ .

To find the number of students in the set $(A \cap)^{\prime}$ , we first need to find the number of students who like Adventure movies and are in the first grade. Then, we subtract this number from the total number of students.

From the table, we see that the total number of students is640 and the number of students who like Adventure movies and are in the first grade is90.
So, $(A \cap)^{\prime} =640 -90$ .