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Draw the logic diagram and truth table for the following expressions,
(I)AB +(BC)'
(2)A(B' +C') BC'?
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Draw the logic diagram and truth table for the following expressions, ...
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Draw the logic diagram and truth table for the following expressions, ...
**Logic Diagram and Truth Table for the Expressions**

To draw the logic diagram and truth table for the given expressions, we will follow the rules mentioned and break down the answer into headings and HTML bullet points.

**1. Expression: AB (BC)'**

**Logic Diagram:**

The logic diagram for the expression AB (BC)' can be represented using two AND gates and one NOT gate, as shown below:

```
----- -----
A ----| | | |
----- / -----
|
B ------------------AND----
|
----- \ -----
C ----| | | |
----- -----
|
NOT
|
OUTPUT
```

**Truth Table:**

To construct the truth table, we will consider all possible combinations of inputs A, B, and C and calculate the output of the expression AB (BC)'.

```
| A | B | C | (BC)' | AB (BC)' |
|---|---|---|-------|----------|
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 |
```

**2. Expression: A(B' C') + BC'**

**Logic Diagram:**

The logic diagram for the expression A(B' C') + BC' can be represented using three AND gates, two OR gates, and two NOT gates, as shown below:

```
----- -----
A ----| | | |
----- / -----
|
B ------------------AND-----
|
----- \ -----
C'----| | | |
----- / -----
|
NOT OR
|
----- \ -----
C'----| | | |
----- -----
|
OR
|
OUTPUT
```

**Truth Table:**

To construct the truth table, we will consider all possible combinations of inputs A, B, and C and calculate the output of the expression A(B' C') + BC'.

```
| A | B | C | B' | C' | A(B' C') | BC' | A(B' C') + BC' |
|---|---|---|----|----|----------|-----|----------------|
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0
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Draw the logic diagram and truth table for the following expressions, (I)AB +(BC)' (2)A(B' +C') BC'?
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