Question

The library has $463$ books dealing with science and $592$ books of fiction. Of these, $37$ are science fiction books. How many books are either science or fiction?

Answer 1

Finding the number of books either in science or fiction:

Given,

The number of science books is $463$.

Out of $592$ books of fiction. Of these, $37$ are science fiction books

So, the number of fiction books alone is $592-37=555$

The number of books either in science or fiction is equal to the sum of the number of science books alone and fiction books alone.

$463+555=1018$

Alternative method:

The number of science books be $A$.

$n\left(A\right)=463$.

The number of fiction books be $B$.

$n\left(B\right)=592$

The number of science fiction books be $A\cap B$.

$n\left(A\cap B\right)=37$

The number of books either in science or fiction be $A\cup B$

We know that

$$\begin{gathered} n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ =463+592-37 \\ =1018 \end{gathered}$$

Hence, the number of books either in science or fiction is$1018$.