Out of a group of 600 students taking computer,mathematics or physics,there is no student taking both computer and mathematics.Every student takes computer or mathematics.150 take physics and mathematics and 250 take only one of the subjects.Find 1) the number of students taking computer and physics. 2) the number of students taking physics.
To solve this problem, we can use a Venn diagram. Let's draw three circles: one for computer, one for mathematics, and one for physics.
1) Let's start by filling in the given information. We know that 150 students take mathematics and physics, and 250 students take exactly one subject. Therefore, we can fill in the overlapping region between mathematics and physics with 150.
_______
| |
Mathematics --|---150-|--
|_______|
2) We also know that no student takes both computer and mathematics, so there is no overlap between these two subjects.
_______ _______
| | | |
Computer -- |-------|
|_______|
3) Now, we need to find the number of students taking computer and physics. We know that a total of 600 students are taking these subjects, and we already found that 150 students take mathematics and physics. So, to find the number of students taking computer and physics, we can subtract the total number of students taking mathematics and physics from the total number of students.
Total students = 600
Students taking mathematics and physics = 150
Students taking computer and physics = Total students - Students taking mathematics and physics
= 600 - 150
= 450
_______
| |
Computer -----|---450-|--
|_______|
4) Finally, we need to find the number of students taking physics. We know that there are 150 students taking mathematics and physics, and 450 students taking computer and physics. These two groups are the only ones taking physics. So, we can add them up to find the total number of students taking physics.
Students taking mathematics and physics = 150
Students taking computer and physics = 450
Students taking physics = Students taking mathematics and physics + Students taking computer and physics
= 150 + 450
= 600
Therefore, the answer to the given problem is:
1) The number of students taking computer and physics is 450.
2) The number of students taking physics is 600.
To find the number of students taking computer and physics, we need to subtract the number of students taking only one of the subjects from the total number of students taking physics.
To find the number of students taking physics, we will add up the number of students taking only physics and the number of students taking both physics and mathematics.
Given information:
- Total number of students (T) = 600
- Number of students taking physics and mathematics (P ∩ M) = 150
- Number of students taking only one subject (Only 1) = 250
Step 1: Find the number of students taking both computer and mathematics (C ∩ M)
- Since no student takes both computer and mathematics, C ∩ M = 0.
Step 2: Calculate the number of students taking physics and computer (P ∩ C)
- To find P ∩ C, we use the formula: P ∩ C = P - (Only 1 + (P ∩ M))
- P ∩ C = 150 - (250 + 150) = 150 - 400 = -250
Since the value is negative, it means there are no students taking both computer and physics.
Step 3: Calculate the number of students taking physics (P)
- To find P, we use the formula: P = (Only 1 + (P ∩ M)) + (P ∩ C)
- P = 250 + (-250) = 0
Therefore, there are no students taking physics.
Final Answers:
1) The number of students taking computer and physics is 0.
2) The number of students taking physics is 0.