PPT - Boolean Logic Truth Tables PowerPoint Presentation, free ... - Free Printable

To solve the problem, we need to fill out the truth tables for each given logical expression. Let's go through each table step by step.

Table 1:

| p | q | ¬p | ¬p and q |
|---|---|----|----------|
| F | F | T | F |
| F | T | T | T |
| T | F | F | F |
| T | T | F | F |

Explanation:
- ¬p: The negation of `p`. If `p` is `F`, then `¬p` is `T`, and vice versa.
- ¬p and q: This is true only if both `¬p` and `q` are true.

Table 2:

| p | q | ¬q | p xor ¬q |
|---|---|----|----------|
| F | F | T | T |
| F | T | F | F |
| T | F | T | T |
| T | T | F | F |

Explanation:
- ¬q: The negation of `q`.
- p xor ¬q: This is true if either `p` or `¬q` is true, but not both.

Table 3:

| p | q | ¬p | ¬q | ¬p or ¬q |
|---|---|----|----|----------|
| F | F | T | T | T |
| F | T | T | F | T |
| T | F | F | T | T |
| T | T | F | F | F |

Explanation:
- ¬p: The negation of `p`.
- ¬q: The negation of `q`.
- ¬p or ¬q: This is true if either `¬p` or `¬q` is true.

Table 4:

| p | q | ¬q | p xor ¬q | (p xor ¬q) and p |
|---|---|----|----------|------------------|
| F | F | T | T | F |
| F | T | F | F | F |
| T | F | T | T | T |
| T | T | F | F | F |

Explanation:
- ¬q: The negation of `q`.
- p xor ¬q: This is true if either `p` or `¬q` is true, but not both.
- (p xor ¬q) and p: This is true only if both `(p xor ¬q)` and `p` are true.

Table 5:

| p | q | r | q and r | p or r | ¬(p or r) | (q and r) or ¬(p or r) |
|---|---|---|---------|--------|-----------|-----------------------|
| F | F | F | F | F | T | T |
| F | F | T | F | T | F | F |
| F | T | F | F | F | T | T |
| F | T | T | T | T | F | T |
| T | F | F | F | T | F | F |
| T | F | T | F | T | F | F |
| T | T | F | F | T | F | F |
| T | T | T | T | T | F | T |

Explanation:
- q and r: This is true only if both `q` and `r` are true.
- p or r: This is true if either `p` or `r` is true.
- ¬(p or r): The negation of `(p or r)`.
- (q and r) or ¬(p or r): This is true if either `(q and r)` or `¬(p or r)` is true.

Table 6:

| p | q | r | p xor q | p xor r | ¬(p xor q) | ¬(p xor q) and (p xor r) |
|---|---|---|---------|---------|------------|--------------------------|
| F | F | F | F | F | T | F |
| F | F | T | F | T | T | T |
| F | T | F | T | F | F | F |
| F | T | T | T | T | F | F |
| T | F | F | T | F | F | F |
| T | F | T | T | T | F | F |
| T | T | F | F | F | T | F |
| T | T | T | F | T | T | T |

Explanation:
- p xor q: This is true if either `p` or `q` is true, but not both.
- p xor r: This is true if either `p` or `r` is true, but not both.
- ¬(p xor q): The negation of `(p xor q)`.
- ¬(p xor q) and (p xor r): This is true only if both `¬(p xor q)` and `(p xor r)` are true.

Final Answer:

The completed truth tables are as follows:

1.
| p | q | ¬p | ¬p and q |
|---|---|----|----------|
| F | F | T | F |
| F | T | T | T |
| T | F | F | F |
| T | T | F | F |

2.
| p | q | ¬q | p xor ¬q |
|---|---|----|----------|
| F | F | T | T |
| F | T | F | F |
| T | F | T | T |
| T | T | F | F |

3.
| p | q | ¬p | ¬q | ¬p or ¬q |
|---|---|----|----|----------|
| F | F | T | T | T |
| F | T | T | F | T |
| T | F | F | T | T |
| T | T | F | F | F |

4.
| p | q | ¬q | p xor ¬q | (p xor ¬q) and p |
|---|---|----|----------|------------------|
| F | F | T | T | F |
| F | T | F | F | F |
| T | F | T | T | T |
| T | T | F | F | F |

5.
| p | q | r | q and r | p or r | ¬(p or r) | (q and r) or ¬(p or r) |
|---|---|---|---------|--------|-----------|-----------------------|
| F | F | F | F | F | T | T |
| F | F | T | F | T | F | F |
| F | T | F | F | F | T | T |
| F | T | T | T | T | F | T |
| T | F | F | F | T | F | F |
| T | F | T | F | T | F | F |
| T | T | F | F | T | F | F |
| T | T | T | T | T | F | T |

6.
| p | q | r | p xor q | p xor r | ¬(p xor q) | ¬(p xor q) and (p xor r) |
|---|---|---|---------|---------|------------|--------------------------|
| F | F | F | F | F | T | F |
| F | F | T | F | T | T | T |
| F | T | F | T | F | F | F |
| F | T | T | T | T | F | F |
| T | F | F | T | F | F | F |
| T | F | T | T | T | F | F |
| T | T | F | F | F | T | F |
| T | T | T | F | T | T | T |

Boxed Final Answer:
\[
\boxed{
\begin{array}{c}
\text{See the filled tables above.}
\end{array}
}
\]