Question

According to De Morga's theorem overbar (X * Y) is equivalent to _____________.

A) Overbar X + overbar Y.
B) Overbar X - overbar Y.
C) X - Y.
D) X + Y.

Answer 1

According to De Morgan's theorem, the complement of the intersection of two sets or events, denoted as ¬(X × Y), is equivalent to the union of their individual complements, which can be symbolically written as ¬X + ¬Y. The correct answer is A.

Step-by-step explanation:

According to De Morgan's theorem, the complement of the intersection of two sets (or the logical negation of a conjunction) is equivalent to the union of their individual complements. Symbolically, it can be expressed as ¬(X ∩ Y) = ¬X ∪ ¬Y, where ¬ stands for the complement or negation, ∩ stands for the intersection (AND operation), and ∪ stands for the union (OR operation). In the context of logic and sets, if we consider 'X' and 'Y' to be two events or propositions, ¬(X × Y) translates to the negation of both X and Y occurring together, which by De Morgan's theorem becomes ¬X + ¬Y. This is because the intersection of sets or the AND operation in logic correlates to multiplication (×), and the union or the OR operation correlates to addition (+).

In terms of logic gates in computers and technology, De Morgan's theorem shows us how a NAND gate (¬(X × Y)) can be constructed using NOR gates (¬X + ¬Y). This understanding is crucial in designing and simplifying digital circuits. In mathematics or logic, for any two elements X and Y, De Morgan's theorem helps in understanding the fundamental properties of operations and their negations.

Answer 2

According to De Morgan's theorem, overbar (X * Y) is equivalent to overbar X + overbar Y, so the correct answer is A) Overbar X + overbar Y.