Given the following sets A and B$,$ determine if each question is true or false, $($provide brief explanation$)$

A$=\{1,2,3\}$

B$=(*,+\}$

a$)(3,+)$ in A X B

b$)(2,*)$ in B X A

c$)$ A $$ A x B

d$)$ B $$ B x A

e$)|$A x B$|=|$B x A$|$