De Morgan’s second theorem states that the complement of the AND of two or more variables is the OR of the complements of those variables. In other words, $(A \land B)’ = A’ \lor B’$.
A NAND gate is a logic gate that implements the logical negation of the AND function. It has two inputs and one output. The output is true if both inputs are false, and false otherwise.
A bubbled AND gate is a logic gate that implements the AND function with a bubble on one of its inputs. The bubble inverts the input, so the output of a bubbled AND gate is true if both inputs are false, and false otherwise.
Therefore, De Morgan’s second theorem says that a NAND gate is equivalent to a bubbled AND gate.
Option A: AND. An AND gate is a logic gate that implements the AND function. It has two inputs and one output. The output is true if both inputs are true, and
false otherwise. A bubbled AND gate is a logic gate that implements the AND function with a bubble on one of its inputs. The bubble inverts the input, so the output of a bubbled AND gate is true if both inputs are false, and false otherwise. Therefore, a NAND gate is not equivalent to an AND gate.Option B: XAND. An XAND gate is a logic gate that implements the exclusive OR function. It has two inputs and one output. The output is true if either input is true but not both, and false otherwise. A bubbled XAND gate is a logic gate that implements the exclusive OR function with a bubble on one of its inputs. The bubble inverts the input, so the output of a bubbled XAND gate is true if both inputs are true or both inputs are false, and false otherwise. Therefore, a NAND gate is not equivalent to an XAND gate.
Option C: XOR. An XOR gate is a logic gate that implements the exclusive OR function. It has two inputs and one output. The output is true if either input is true but not both, and false otherwise. A bubbled XOR gate is a logic gate that implements the exclusive OR function with a bubble on one of its inputs. The bubble inverts the input, so the output of a bubbled XOR gate is true if both inputs are true or both inputs are false, and false otherwise. Therefore, a NAND gate is not equivalent to an XOR gate.
Option D: OR. An OR gate is a logic gate that implements the OR function. It has two inputs and one output. The output is true if either input is true, and false otherwise. A bubbled OR gate is a logic gate that implements the OR function with a bubble on one of its inputs. The bubble inverts the input, so the output of a bubbled OR gate is true if both inputs are false, and false otherwise. Therefore, a NAND gate is not equivalent to an OR gate.
Option E: None of the above.