You're assigning not checking.
That is, you meant "==", not "=".
You want to use the "eq" operator for strings anyway, so change.
You also want to use a scalar, not an array.
Corrections:

$quearyand = new CGI;
$array_and = $queryand->param('option_and');
$array_or = $queryand->param('option_or');
if ($array_and eq "AND") {
    print ....
}
if ($array_or eq "OR") {
    print ...
}
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