Let $(A,s)$ be a partial order with two minimal elements $a,b$ and a maximum element $c.$ Let $,$ False$\}$ be a predicate defined on $A.$

Suppose that $P(a)=$ True, $P(b)=$ False and $P(a)=>P(b)$ for all satisfying $ab,$ where $=>$ stands for logical implication: Which of the following statements is false.

$P(x)=$ True for all $x5$ such that $xb$

$P(x)=$ False for all xinS such that $x$a and $xc$

$P(x)=$ False for all xinS such that $ax$ and $bx$

$P(x)=$ False for all xinS such that $bx$ and $xc$