Solve the mystery using LOGIC COMPUTER SCIENCE

The famous detective, Inspector Percule Hoirot, was summoned to unravel

the perplexing case of the stolen Azure Diamond from the grand estate of

Duke Wellington. Amidst a gathering of distinguished guests and estate

staff, the diamond vanished under mysterious circumstances. Inspector

Solve gathered the following clues to identify the thief:

$($a$)$ The Azure Diamond was stolen from the safe in the library.

$($b$)$ Either Duchess Wellington or the librarian, Emma, was in the library

at the time of the theft.

$3$

$($c$)$ If the gardener was in the garden at the time of the theft, then the

secretary stole the Azure Diamond using a duplicate key.

$($d$)$ If Duchess Wellington was in the library at the time of the theft, then

the security officer is the thief.

$($e$)$ If the gardener was not in the garden at the time of the theft, then

Emma was not in the library.

$($f$)$ If Emma was in the library at the time of the theft, then the house$-$

keeper is the thief.

Is it possible for Inspector to deduce the identity of the thief from these

clues? If so$,$ who stole the Azure Diamond? Assume there was only one

thief. TIP: Convert the statements in symbolic $($premises$)$ and use valid

argument forms to deduce the conclusion from the premises.

$4($c$)$ If the gardener was in the garden at the time of the theft, then the

secretary stole the Azure Diamond using a duplicate key.

$($d$)$ If Duchess Wellington was in the library at the time of the theft, then

the security officer is the thief.

$($e$)$ If the gardener was not in the garden at the time of the theft, then

Emma was not in the library.

$($f$)$ If Emma was in the library at the time of the theft, then the house$-$

keeper is the thief.

Is it possible for Inspector to deduce the identity of the thief from these

clues? If so$,$ who stole the Azure Diamond? Assume there was only one

thief. TIP: Convert the statements in symbolic $($premises$)$ and use valid

argument forms to deduce the conclusion from the premises.