Question 14: We are given a single-input NAND gate and a truth table where the output $Q$ is represented by $X$ when the input $A$ is 0, and $Y$ when $A$ is 1. We need to find the correct values of $X$ and $Y$. Question 15: We are given a logic circuit built using NAND, NOR, and NOT gates. We need to determine which Boolean expression is equivalent to the output $Q$ of this circuit. Question 16: We are given three statements about operating systems and user interfaces. We need to identify which of these statements are correct.

1. Problem Description

Question 14: We are given a single-input NAND gate and a truth table where the output $Q$ is represented by $X$ when the input $A$ is 0, and $Y$ when $A$ is

1. We need to find the correct values of $X$ and $Y$.

Question 15: We are given a logic circuit built using NAND, NOR, and NOT gates. We need to determine which Boolean expression is equivalent to the output $Q$ of this circuit.

Question 16: We are given three statements about operating systems and user interfaces. We need to identify which of these statements are correct.

2. Solution Steps

Question 14:

A NAND gate performs the AND operation and then negates the result. In a single-input NAND gate, the output $Q$ is the negation of the input $A$.

If $A = 0$, then $Q = \overline{0} = 1$. So $X = 1$.

If $A = 1$, then $Q = \overline{1} = 0$. So $Y = 0$.

The correct values for $X$ and $Y$ are 1 and 0 respectively.

Question 15:

Let's analyze the given circuit.

The inputs are $A$ and $B$.

First NAND gate's output is $\overline{A \cdot B}$.

Second NAND gate's output is $\overline{A \cdot B}$.

These two outputs are connected to the inputs of the NOR gate.

So, the NOR gate's output is $\overline{\overline{A \cdot B} + \overline{A \cdot B}}$.

The inverter (NOT gate) at the end negates the NOR gate's output.

So, $Q = \overline{\overline{\overline{A \cdot B} + \overline{A \cdot B}}} = \overline{\overline{\overline{A \cdot B}}} = \overline{A \cdot B}$.

Now we need to simplify this expression. The NAND operation is defined as

$\overline{A \cdot B} = \overline{A} + \overline{B}$ by DeMorgan's Law.

So $Q = \overline{A \cdot B}$.

Now let's check the provided options:

1) $\overline{A}B + A\overline{B}$

2) $\overline{AB + AB} = \overline{AB}$. Because $AB+AB=AB$.

3) $\overline{AB} + \overline{AB}$

4) $AB + AB = AB$

We have found that $Q = \overline{A \cdot B}$. Therefore the correct answer is option

2.

Question 16:

Statement A: Ubuntu is a free and open-source operating system. This is correct.

Statement B: MS-DOS is a single-user operating system. This is correct.

Statement C: Command Line Interface (CLI) is more user-friendly than Graphical User Interface (GUI). This is incorrect. GUIs are generally considered more user-friendly.

Therefore, statements A and B are correct.

3. Final Answer

Question 14: 4) 1,0

Question 15: 2) $\overline{AB + AB}$

Question 16: 3) A,B Only