EXOR gate is an odd number of $1’s$ detector. It gives $0$ as output for the same input and for different input it gives $1$ as output, also the EXOR logic gate is left-associative.
- $1\oplus 0=1:$ This is true, different input,so output is $1.$
- $1\oplus 1\oplus 0=1:$ It can be written as: $((1\oplus 1)\oplus 0)\implies(0\oplus 0)=0\neq1$,so this options is false.
- $1\oplus 1\oplus 1=1$: $((1\oplus 1)\oplus 1)\implies (0\oplus 1)=1$,so this is true.
- $1\oplus 1=0$: This is true, for the same input value EXOR gate gives $0$ as output.
So Option $(B)$ is incorrect.