Let A $=\{1,4,5\}$ and B $=\{4,6,7\}.$

$1.$ Select all the cartesian products that $(5,6)$ is an element of$.$ There may be more than one correct answer.

A$.$ A $*$ B

B$.$ A $*$ A

C$.$ B $*$ A

D$.$ B $*$ B

$2.$ Select all the cartesian products that $(7,4)$ is an element of$.$ There may be more than one correct answer.

A$.$ B $*$ A

$.*$ B

C$.$ A $*$ A

D$.$ B $*$ B

$3.$ Select all the cartesian products that $(4,4)$ is an element of$.$ There may be more than one correct answer.

A$.$ A $*$ B

B$.*$

C$.*$

D$.$ B $*$ A

$4.$ Select all the cartesian products that $(1,1)$ is an element of$.$ There may be more than one correct answer.

$.*$

B$.*$

C$.$ B $*$ A

D$.$ A $*$ A