Describe the conditions under which the statement is true.
-$\mathrm { A } \cap \mathrm { A } ^ { \prime } = \mathrm { A }$
A) $\mathrm { A } = \mathrm { U }$
B) Always true
C) $A \neq \varnothing$
D) $A = \varnothing$

Question

Quizplus · Accepted Answer

The statement $A \cap A' = A$ is never true because $A \cap A'$ represents the intersection of set A and its complement, which is always the empty set $\varnothing$, not A. The correct condition is $A = \varnothing$ because the intersection of the empty set with its complement (the universal set) is indeed the empty set, which matches the right side of the equation.

Describe the Conditions Under Which the Statement Is True A∩A′=A\mathrm { A } \cap \mathrm { A } ^ { \prime } = \mathrm { A }A∩A′=A

Describe the Conditions Under Which the Statement Is True $\mathrm { A } \cap \mathrm { A } ^ { \prime } = \mathrm { A }$