The problem consists of three parts: (a) Write down the Boolean expression for the given logic circuit. (b) Prove the Boolean expression $A \cdot \overline{B} + B = A + B$ using a truth table. (c) Identify the slide layout/office theme from the given options. (d) Find the letter corresponding to the formatting for different text attributes.

1. Problem Description

The problem consists of three parts:

(a) Write down the Boolean expression for the given logic circuit.

(b) Prove the Boolean expression $A \cdot \overline{B} + B = A + B$ using a truth table.

(c) Identify the slide layout/office theme from the given options.

(d) Find the letter corresponding to the formatting for different text attributes.

2. Solution Steps

(a) The logic circuit consists of an inverter, AND gates, and an OR gate.

The input $B$ goes through an inverter, so the output is $\overline{B}$.

The inputs $A$ and $\overline{B}$ are fed into an AND gate, so the output is $A \cdot \overline{B}$.

The inputs $C$ and $B$ are fed into an AND gate, so the output is $C \cdot B$.

The outputs of the two AND gates are fed into an OR gate, so the final output $Q$ is $A \cdot \overline{B} + C \cdot B$.

(b) To prove $A \cdot \overline{B} + B = A + B$ using a truth table, we need to consider all possible values of $A$ and $B$ (0 and 1).

Truth Table:

| A | B | $\overline{B}$ | $A \cdot \overline{B}$ | $A \cdot \overline{B} + B$ | A + B |

|---|---|---|---|---|---|

| 0 | 0 | 1 | 0 | 0 | 0 |

| 0 | 1 | 0 | 0 | 1 | 1 |

| 1 | 0 | 1 | 1 | 1 | 1 |

| 1 | 1 | 0 | 0 | 1 | 1 |

From the truth table, we can see that the values of $A \cdot \overline{B} + B$ and $A + B$ are the same for all possible values of $A$ and $B$. Therefore, $A \cdot \overline{B} + B = A + B$ is proven.

(c) The given slide has a title and some content. This corresponds to option (B), which is "Title and content".

(d)

1: The text "27th September 2019" is underlined. The corresponding tool is 'C'.

2: The "Sri Lanka" is written in italics. The corresponding tool is 'B'.

3: The "S" is larger than the rest of the text. This is called drop cap. There is no corresponding letter for drop cap in the given set of tools.

4: The paragraph is left-aligned. The corresponding tool is 'I'.

11: It is the size of the font. There is no corresponding letter for font size.

3. Final Answer

(a) $Q = A \cdot \overline{B} + C \cdot B$

(b) Proven by the truth table in Solution Steps.

(c) (B) Title and content

(d)

1: C

2: B

3: No corresponding letter.

4: I

11: No corresponding letter.