there are 50 pupils in a class. 43 of them like mathematics, 38 like english and 33 like both mathematics and english. How many pupils like both mathematics and english??

Umm, didn't you just say that 33 like both?

To find out how many pupils like both mathematics and English, you can use the concept of set theory.

Let's represent the set of pupils who like mathematics as M, the set of pupils who like English as E, and the set of pupils who like both mathematics and English as B.

According to the given information, the number of pupils who like mathematics is 43, the number of pupils who like English is 38, and the number of pupils who like both subjects is 33.

We can use the principle of inclusion-exclusion to determine the number of pupils who like both mathematics and English.

According to this principle, the formula is as follows:
| M ∪ E | = | M | + | E | - | M ∩ E |

To find out the number of pupils who like both subjects, substitute the given values into the formula:
| M ∩ E | = | M | + | E | - | M ∪ E |
= 43 + 38 - 50

When you calculate this expression, you will find that 31 pupils like both mathematics and English.