Answer:
To solve this problem using a Venn diagram, we start by drawing two overlapping circles to represent the set of students who passed in math and the set of students who passed in physics. We label the overlapping region as the set of students who passed in both math and physics, which is given as 62 in the problem. We also know that four students failed in both math and physics, and seven students only failed in math. We can use this information to fill in the Venn diagram and answer the questions:
i. To find the number of students who failed in physics only, we need to look at the part of the physics circle that does not overlap with the math circle. From the diagram, we can see that this number is (35 - 4) = 31.
ii. To find the number of students who passed in math, we need to add up the number of students in the math-only circle and the math-and-physics overlap region. From the diagram, we can see that this number is (23 + 62) = 85.
iii. To find the number of students who passed in physics, we need to add up the number of students in the physics-only circle and the math-and-physics overlap region. From the diagram, we can see that this number is (31 + 62) = 93.
Therefore, the answers to the three questions are:
i. 31 students failed in physics only
ii. 85 students passed in mathematics
iii. 93 students passed in physics.