The following dividend theories are listed:

a$)$ Agency cost theory suggest that firms with high cash flows should make high dividend pay$-$outs.

b$)$ Miller$-$Modigliani irrelevance theory points that initiating or decreasing dividends is perceived as good news by the market and results in an increase in share price.

c$)$ Bird$-$in$-$hand theory. This theory means that investors prefer firms that currently pay dividends than those firms that retain earnings and pay dividends in the future.

d$)$ Investors that have their expectations and preferences on the dividend pay$-$out policy is referred to as the clientele effect on dividend theory

e$)$ The tax preference theory is the dividend policy in a perfect capital market and changes thereto have no impact on the shareholder value.

Which statements above are FALSE?

$1.$

Statements $($b$)$ and $($e$)$

$2.$

Statements $($d$)$ and $($e$)$

$3.$

Statements $($a$),($c$)$ and $($e$)$

$4.$

Statements $($a$)$ and $($b$)$