in a class of 60 student,26 offer mathmatic and 28 offer physics if 8 student do not offer any of the two subject
(1)how many student offer both subject.
(2)how many student offer mathematic only.
(3)how many student offer physics only.
(4)how many student offer only one subject.set theory
in a class of ,26 offer mathmatic and 28 offer physics if 8 student do not offer any of the two subject
This means that there are 60-8=52 students take at least one subject.
Since total number of subjects taken is 26 and 28=54, we know that 54-52=2 students take both.
I'll leave it to you to calculate how many take only math and only physics.
To solve this problem using set theory, we can start by visualizing the problem with a Venn diagram. Let's define two sets: M for students who offer math and P for students who offer physics.
Given information:
Total number of students in the class (60)
Number of students who offer math (26)
Number of students who offer physics (28)
Number of students who do not offer either subject (8)
Using the given information, we can fill in the Venn diagram as follows:
```
M
__/ \__
/ \
\_______/
P
```
Now, we can solve each part of the problem:
(1) Number of students who offer both subjects:
To find the overlap between the two sets M and P, we can subtract the number of students who do not offer either subject from the total number of students:
Number of students who offer both subjects = Total number of students - Number of students who do not offer either subject
Number of students who offer both subjects = 60 - 8
Number of students who offer both subjects = 52
(2) Number of students who offer mathematics only:
To find the number of students who offer math only, we can subtract the overlap (students who offer both subjects) from the number of students who offer math:
Number of students who offer math only = Number of students who offer math - Number of students who offer both subjects
Number of students who offer math only = 26 - 52
Number of students who offer math only = 0
(3) Number of students who offer physics only:
To find the number of students who offer physics only, we can subtract the overlap (students who offer both subjects) from the number of students who offer physics:
Number of students who offer physics only = Number of students who offer physics - Number of students who offer both subjects
Number of students who offer physics only = 28 - 52
Number of students who offer physics only = 0
(4) Number of students who offer only one subject:
To find the number of students who offer only one subject, we can add the number of students who offer math only and the number of students who offer physics only:
Number of students who offer only one subject = Number of students who offer math only + Number of students who offer physics only
Number of students who offer only one subject = 0 + 0
Number of students who offer only one subject = 0
In summary:
(1) Number of students who offer both subjects = 52
(2) Number of students who offer math only = 0
(3) Number of students who offer physics only = 0
(4) Number of students who offer only one subject = 0