The relation $\leq$ and $>$ on a boolean algebra are defined as:
$x \leq y$ if and only if $x \vee y =y$
$x <y$ means $x \leq y$ but $x \neq y$
$x \geq y$ means $y \leq x$ and
$x>y$ means $y<x$
Considering the above definitions, which of the following is not true in the boolean algebra?
- If $x \leq y$ and $y \leq z$, then $x \leq z$
- If $x \leq y$ and $y \leq x$, then $x = y$
- If $x < y$ and $y < z$, then $x \leq y$
- If $x < y$ and $y < z$, then $x < y$
Choose the correct answer from the code given below:
- i and ii only
- ii and iii only
- iii only
- iv only