Answer: This data can be proven to be incorrect using the Principle of Inclusion-Exclusion.
The Principle of Inclusion-Exclusion states that for two events A and B, the number of elements in the union of A and B is equal to the sum of the number of elements in A and the number of elements in B minus the number of elements in their intersection.
Let's denote the number of students who failed in Maths as M, Accounts as A, and Costing as C.
From the information given, we have the following relationships:
M = 750
A = 600
C = 600
A ∩ C = 150
M ∩ A = 450
M ∩ C = 400
M ∩ A ∩ C = 75
Applying the Principle of Inclusion-Exclusion, the number of students who failed in at least one subject is:
M + A + C - (A ∩ C) - (M ∩ A) - (M ∩ C) + (M ∩ A ∩ C) = 750 + 600 + 600 - 150 - 450 - 400 + 75 = 925
However, the number of students who appeared for the exams is 1000, which means that the number of students who passed in all subjects should be 1000 - 925 = 75.
But we have already determined that the number of students who failed in all subjects is 75, which means that there are 75 students who are counted twice. This leads to a contradiction, and therefore the data given cannot be correct.
Explanation: