How to check if a variable is set in Bash
if [ -z ${var+x} ]; then echo "var is unset"; else echo "var is set to '$var'"; fi
where ${var+x} is a parameter expansion1 which evaluates to nothing if var is unset, and substitutes the string x otherwise.
Quotes can be omitted (so we can say ${var+x} instead of "${var+x}") because this syntax & usage guarantees this will only expand to something that does not require quotes (since it either expands to x (which contains no word breaks so it needs no quotes), or to nothing (which results in [ -z ], which conveniently evaluates to the same value (true) that [ -z "" ] does as well)).
However, while quotes can be safely omitted, and it was not immediately obvious to all, it would sometimes be better to write the solution with quotes as [ -z "${var+x}" ], at the very small possible cost of an O(1) speed penalty.