$1.$ Let us define X$=$Alan Turing is allergic to pollen$,$ Y$=$Alan Turing is wearing a mask$$ and Z$=$The rose garden has a lot of flowers$.$ Translate the statements into propositional logic $(10$ Points$)$

$($a$)$ Alan Turing is not allergic to pollen and he is wearing a mask

$($b$)$ If Alan Turing is allergic to pollen and the rose garden has a lot of flowers then he will be wearing a mask

$($c$)$ Exactly one of the following two things must be true $-$ either the rose garden has a lot of flowers or Alan Turing is not wearing a mask $($do not use XNOR or XOR$)$