Basic Logic Gate Output Waveform/XOR and XNOR gate/Digital Logic Design

The Exclusive OR (or XOR) relationship
F=A⊕B
XOR is an odd detector, and the XNOR an even detector.
The XOR output is asserted whenever an odd number of inputs are asserted, and the XNOR is asserted whenever an even number of inputs are asserted: the XOR is an odd detector, and the XNOR, an even detector.
Any odd number of input inversion changes the function output between the XOR and XNOR functions; any even number of input signal inversions does not change function outputs; any three input signal inversions changes the function output
Xor gate can be used as a “controlled inverter”.
The algebraic notation used to represent the XNOR operation is