Question

For every rational numbers $x,y$ and $z$, $x+\left(y\times z\right)=\left(x+y\right)\times \left(x+z\right)$.

State whether the statement is true or false.

• A. True
• B. False

Answer 1

The correct option is B False

Distributive property of multiplication:

According to the distributive property of multiplication over addition,

$a\times \left(b+c\right)=\left(a\times b\right)+\left(a\times c\right)$

So, $a+\left(b\times c\right)\ne \left(a\times b\right)+\left(a\times c\right)$

$x+\left(y\times z\right)=\left(x+y\right)\times \left(x+z\right)$

Hence, the given statement is false.