Suppose that $$n in N$,$ A

n

$=$ and m $$ n $=$ A

m

$$ A

n

$.$ Prove or disprove the following:

$($a$)$

$293$

S

n$=1$

A

n

$=($b$)$

$293$

T

n$=1$

A

n

$=($c$)$

S

n in N

A

n

$=($d$)$

T

n in N

A

n

$=$