The binary operator $$ \ne $$ is defined by the following truth table.

p	q	p$$ \ne $$q
0	0	0
0	1	1
1	0	1
1	1	0

Which one of the following is true about the binary operator $$ \ne $$?

Let $$ \oplus $$ denote the exclusive $$OR\left( {XOR} \right)$$ operation. Let $$'1'$$ and $$'0'$$ denote the binary constants. Consider the following Boolean expression for $$F$$ over two variables $$P$$ and $$Q$$:
$$F\left( {P,Q} \right) = \left( {1 \oplus P} \right) \oplus \left( {P \oplus Q} \right) \oplus \left( {P \oplus Q} \right) \oplus \left( {Q \oplus 0} \right)$$

The equivalent expression for $$F$$ is

What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?

If $$P, Q, R$$ are Boolean variables, then $$\left( {P + \overline Q } \right)$$ $$\left( {P.\overline Q + P.R} \right)\left( {\overline P .\overline R + \overline Q } \right)$$ Simplifies to