The conditional check is not being executed it just prints the echo statement for legit input [duplicate]

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• Why non-equality check of one variable against many values always returns true? 3 answers

read a
if [[ $a != 'A' || $a != 'a']] && [[ $a != 'B' || $a != 'b' ]] && [[ $a !='C' || $a != 'c']]; then 
       echo "ABC only"
fi