In a class of 25 boys, 19 have English books, 17 have French, and 15 have Math. Given the intersections, find the number of boys with all three types of books.

This problem involves set theory and Venn diagrams. Let $E$ represent the set of boys with English books, $F$ for French books, and $M$ for Mathematics books. The total number of boys in the class is $N = 25$.

Given information:

• $|E| = 19$
• $|F| = 17$
• $|M| = 15$
• $|E \cap F| = 16$
• $|F \cap M| = 11$
• $|E \cap M| = 13$

We need to find the number of boys in the intersection of all three sets, $|E \cap F \cap M