Question

Is it possible to use a logical AND in a unix shell script switch case. If so, how?

switch $var in
    1 AND $var2 EQUALS 2)
        some code

Answer 1

You need to use if statements for that.

See this.

“Each case is an expression matching a pattern. The commands in the
COMMAND-LIST for the first match are executed. The “|” symbol is used
for separating multiple patterns, and the “)” operator terminates a
pattern list. “

So you need to have patterns, not an expression to be evaluated, for each case.