For which of the following Boolean expression | vedclass

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(A) We evaluate each expression for $A=0$ and $A=1$:$(A)$ $A \cdot \overline{A}$:For $A=0$: $0 \cdot \overline{0} = 0 \cdot 1 = 0$.For $A=1$: $1 \cdot

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$A \cdot \overline{A}$

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(A) We evaluate each expression for $A=0$ and $A=1$:$(A)$ $A \cdot \overline{A}$:For $A=0$: $0 \cdot \overline{0} = 0 \cdot 1 = 0$.For $A=1$: $1 \cdot \overline{1} = 1 \cdot 0 = 0$.Since the result is $0$ for both cases,this expression is always zero.$(B)$ $A \cdot 0$:For $A=0$: $0 \cdot 0 = 0$.For $A=1$: $1 \cdot 0 = 0$.This expression is also always zero.$(C)$ $\overline{A + \overline{A}}$:For $A=0$: $\overline{0 + \overline{0}} = \overline{0 + 1} = \overline{1} = 0$.For $A=1$: $\overline{1 + \overline{1}} = \overline{1 + 0} = \overline{1} = 0$.This expression is also always zero.$(D)$ $\overline{\overline{A} \cdot 0}$:For $A=0$: $\overline{\overline{0} \cdot 0} = \overline{1 \cdot 0} = \overline{0} = 1$.For $A=1$: $\overline{\overline{1} \cdot 0} = \overline{0 \cdot 0} = \overline{0} = 1$.This expression is always $1$.Note: Options $A$,$B$,and $C$ are mathematically equivalent to $0$ in Boolean algebra. In standard multiple-choice contexts,$A \cdot \overline{A}$ is the fundamental identity for zero.

For which of the following Boolean expressions is the result always zero?

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