A 'literal' in Boolean Algebra means

The correct answer is B, OR. Read the table row by row. The output is 0 only when both inputs are 0, and it is 1 in the other three rows, including the row where both inputs are 1. That is exactly the rule of an OR gate, which gives 1 when at least one input is 1 and behaves like two switches wired in parallel. A is wrong because a NOT gate has only one input and so cannot have a table with two input columns at all. C is wrong because an XOR gate responds only to a difference between its inputs, so its last row, with both inputs 1, would give 0 and not 1; this is the one row that separates OR from XOR and the reason the distractor is offered. D is wrong because an AND gate gives 1 only in the last row and 0 in the first three, which is the mirror image of the table shown.

The correct answer is B, NAND and NOR. Each of these gates alone is enough to build every other gate and so every logic circuit: a NAND with its two inputs tied together acts as a NOT, two NANDs in sequence give an AND, and a suitable arrangement of three gives an OR, and the same can be done entirely with NOR gates. That is why chip makers sell packages containing only one gate type. A is wrong because AND and OR cannot produce a complement by themselves; without a NOT they can never invert a signal. C is wrong because XOR and XNOR are themselves derived gates, built from the basic three, and neither can generate the full set on its own. D is wrong because NOT with AND can indeed build everything, but the pair is not given the name universal gates; the term is reserved for the two single gates that suffice by themselves.

The correct answer is B, the sum of the complements. De Morgan's second theorem states that NOT of A AND B equals NOT A OR NOT B. The working rule is to break the bar and change the sign, so a dot under a complement becomes a plus once the complement is distributed over the variables. A is wrong because the product of the complements is the result of the first theorem, which applies to the complement of a sum, not of a product; swapping the two theorems is the standard error in this question. C is wrong because complementing an expression must change it unless the expression is a constant, and the product of A and B is not its own complement. D is wrong because the value depends on the inputs: when A is 1 and B is 1 the expression is 0, so it cannot always be 1. Both theorems together make NAND-only and NOR-only design possible.

The correct answer is C, when the two inputs are different. An exclusive OR gate is a difference detector: it gives 1 for the combinations 0 and 1 or 1 and 0, and gives 0 when the inputs agree. It is sometimes read as either but not both. A is wrong because two inputs of 1 give an output of 0 in an XOR gate; that row is exactly what distinguishes it from an ordinary OR gate, which would give 1. B is wrong because two inputs of 0 also agree, so the output is again 0. D is wrong because an output of 1 for identical inputs describes the XNOR gate, the complement of XOR, which works as an equality detector and is used to compare two binary numbers bit by bit. In a half adder, the XOR gate supplies the sum bit while the AND gate supplies the carry.

The correct answer is B, George Boole, the English mathematician who in the middle of the nineteenth century showed that logical reasoning could be written as an algebra on just two values, true and false. The system was a work of pure mathematics for decades until Claude Shannon showed that it described electrical switching circuits exactly, which opened the way to digital computing. A is wrong because Charles Babbage designed the Difference Engine and the Analytical Engine and is called the father of the computer, but he worked on mechanical calculation, not on logic as algebra. C is wrong because Blaise Pascal built an early mechanical adding machine, the Pascaline, in the seventeenth century. D is wrong because John von Neumann gave the stored-program architecture in which instructions and data share the same memory, a much later contribution. Pair the names carefully: Boole for the algebra, Shannon for its use in circuits, Karnaugh for the simplification map.