Decide whether the given statement is always true or not always true.
-$\mathrm { A } \cup ( \mathrm { B } \cap \mathrm { C } ) ^ { \prime } = \mathrm { A } \cup \left( \mathrm { B } ^ { \prime } \cup \mathrm { C } ^ { \prime } \right)$
A) Not always true
B) Always true

Question

Quizplus · Accepted Answer

The statement is always true due to De Morgan's laws, which state that the complement of the intersection of two sets is equal to the union of their complements. Thus, $(B \cap C)^\prime = B^\prime \cup C^\prime$, making the equation true.

Decide Whether the Given Statement Is Always True or Not