Let

$>$

$=$

be a weak preference that is complete, reflexive, and transitive. In the

class, we defined, based on

$>$

$=$

$,$

$($

a

$)$

$$the indifference relation

$$

$$as: B

$1$

$$

$$B

$2$

$$if

B

$1$

$>$

$=$

B

$2$

$$and B

$2$

$>$

$=$

$$B

$1$

; and

$($

b

$)$

$$the strict preference relation

$>$

as: B

$1$

$>$

B

$2$

$$if

B

$1$

$>$

$=$

B

$2$

$$and B

$2$

$$ not

$>$

$=$

B

$1$

$.$

$($

i

$)$

is $>$ complete, reflexive, and transitive?