Determine whether the set $A \cap U$ is equal to $\varnothing, A$, or $U$. Assume $A \neq \varnothing$ and $A \neq U$.

Choose the correct answer below.
A. $A \cap U=A$
B. $A \cap U=U$
C. $A \cap U=\varnothing$

Answer

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Answer

$\boxed{A \cap U=A}$

Steps

Step 1 ：The intersection of a set A and a universal set U, denoted as $A \cap U$, is the set of all elements that are common to both A and U.

Step 2 ：Since A is a subset of U (because every set is a subset of the universal set), every element of A is also an element of U.

Step 3 ：Therefore, the intersection of A and U is just the set A itself.

Step 4 ：$\boxed{A \cap U=A}$