Suppose the following table for encoding and decoding and answer the questions.

$\backslash$table$[[$Letter$,$A$,$E$,$Y$,$M$,$O$,$R$,$H$,$L$],[$Binary$,0000,0001,0010,0011,0100,0101,0110,0111],[$Letter$,$F$,$G$,$W$,$N$,$Z$,$I,S$,$P$],[$Binary$,1000,1001,1010,1011,1100,1101,1110,1111]]$

a$.$ Based on the last digit of your CWID, D$\_8,$ circle the message as your plaintext.

$\backslash$table$[[$D$\_8,$Message$],[1,$PALMER$],[2,$SHOWER$],[3,$SYMBOL$],[4,$GROWTH$],[5,$SHINEZ$],[6,$MINGLE$],[7,$LAPDOG$],[8,$SAMPLE$],[9,$HINGES$],[0,$FORMAL$]]$

b$.$ Assume the key is 'INFORM'. What is the ciphertext C$?$ Show the detailed steps.

c$.$ Decrypt the ciphertext got in Problem $5.$b$.$ using key $=$ 'POWERS' and explain the result.