## Problem 3

On the set of real numbers $\mathbb{R}$, the composition law "*" is defined with the following properties:

1) $\left(\frac{a+1}{3}\right) *\left(\frac{a}{2}\right)=1, \forall a \in \mathbb{R}$
2) $(a * b) \cdot c=(a \cdot c) *(b \cdot c), \forall a, b, c \in \mathbb{R}$.

Calculate $10 * 14$.
## Problem 3

$10 * 14=(5 \cdot 2) *(7 \cdot 2)=(5 * 7) \cdot 2 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$
In prop 1) for $a=14 \Rightarrow \frac{15}{3} * \frac{14}{2}=5 * 7=1 \Rightarrow 10 * 14=1 \cdot 2=2$

$3 p$