A "Don't care" or "X" for synthesis means the ignore the input when computing the output. You can't synthesize logic that both ignores the input and also looks at the input at the same time.
What you are asking would make more sense if there were two inputs
input1 = 1, input2 = 1, output = 1;
input1 = 1, input2 = 0, output = 0;
input1 = 0, input2 = x, output = 1;
That third line is saying we don;t care what the value of input2 is, so we could have written it as these two lines instead.
input1 = 0, input2 = 0, output = 1;
input1 = 0, input2 = 1, output = 1;
The synthesized logic for this would be
output = !(input1) || input2;