Question

Which of the following is a form of DeMorgan's theorem?

a) (X+Y)'=X'+Y'
b) X(1)=X
c) (XY)'=X'+Y'
d) X+0=0

Answer 1

DeMorgan's theorem is expressed as (X+Y)' = X'Y'. It states that the complement of a union is equal to the intersection of the complements.

Step-by-step explanation:

The correct form of DeMorgan's theorem is: (X+Y)' = X'Y'.

This theorem states that the complement of a union (X+Y) is equal to the intersection of the complements (X'Y'). In other words, when you take the complement of an expression with multiple terms connected by OR, it is equivalent to taking the complement of each term and then connecting them with AND.

For example, if X represents 'it is raining' and Y represents 'it is sunny', then the complement of (X+Y) (it is raining or it is sunny) is equivalent to the complement of X (it is not raining) AND the complement of Y (it is not sunny). So, (X+Y)' = X'Y'.