Question

simplify (AnB) U (AnB')

Answer 1

Given

The expression is given

(AnB) U (AnB')​

Explanation

Simplified the expression.

$\left(AnB\right)U(AnB^{\prime})$

Apply the distributive law,

$\left(AnB\right)U(AnC)=A\cap(B\cup C)$

Then we get,

$\begin{gathered} (A\cap B)\cup(A\cap B^{\prime})=A\cap(B\cap B^{\prime}) \\ (A\operatorname{\cap}B)\cup(A\operatorname{\cap}B^{\prime})=A\operatorname{\cap}U \\ (A\operatorname{\cap}B)\cup(A\operatorname{\cap}B^{\prime})=A \end{gathered}$

Answer

After simplification, we get A.

The answer is A.