There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.
According to question, $a + b + c + d + e + f + g + h=100$ ...(i) $h=1$ ...(ii) $a + b + d +e=50$ ...(iii)
Venn diagram shows failed students $b + c + d +f=45$ ...(iv) $d + e + f +g=40$ ...(v) $b + e +f=32$ ...(vi) On solving, the above equations, we get $d=2$
In mathematics, a set is a well-defined collection of objects. Sets are named and demonstrated using capital letter. In the set theory, the elements that a set comprises can be any sort of thing: people, numbers, letters of the alphabet, shapes, variables, etc.
The items existing in a set are commonly known to be either elements or members of a set. The elements of a set are bounded in curly brackets separated by commas.
