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Two binary operations $\oplus$ and $*$ are defined over the set $\{a, e, f, g, h\}$ as per the following tables

$\oplus$

a

e

f

g

h

a

a

e

f

g

h

e

e

f

g

h

a

f

f

g

h

a

e

g

g

h

a

e

f

h

h

a

e

f

g

 

$\ast$

a

e

f

g

h

a

a

a

a

a

a

e

a

e

f

g

h

f

a

f

h

e

g

g

a

g

e

h

f

h

a

h

g

f

e

Thus, according to the first table $f \oplus g = a$, while according to the second table $g \ast h=f$, and so on. Also, let $f^2 = f \ast f, \: g^3 = g \ast g \ast g$, and so on.

Upon simplification, $\{ a10 \ast (f10 \oplus g9)\} \oplus e^8$ equals

  1. $e$
  2. $f$
  3. $g$
  4. $h$
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