During lecture we briefly talked about the XOR gate, which is used to output the carry bit in Half Adders. This gate corresponds to the "exclusive or" operation, which is typically signified with a cross inscribed within a circle: (\oplus in LATEX). The truth table and symbol of this gate are both shown in table 2: The negation of the "exclusive or" operation is colloquially referred to as "exclusive not or", and the relevant gate is known as the XNOR gate (see Table 3). There are multiple logical operators used out there for the "exclusive not-or" operation: we will use the symbol (\otimes in LATEX) to denote this operation in boolean logic. (a) Show that the XOR gate can be implemented using the circuit shown in figure 1: (b) Remember the NAND gates from the previous homework? Good. Transform the circuit shown in figure 1 into one that uses ONLY NAND gates! (c) Show that (a b) (a doubleheadarrow b)