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Step-by-step solution for: PPT - Boolean Logic Truth Tables PowerPoint Presentation, free ...
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Show Answer Key & Explanations
Step-by-step solution for: PPT - Boolean Logic Truth Tables PowerPoint Presentation, free ...
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.
| 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.
| 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.
| 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.
| 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.
| 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.
| 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.
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:
\[
\boxed{
\begin{array}{c}
\text{See the filled tables above.}
\end{array}
}
\]
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:
\[
\boxed{
\begin{array}{c}
\text{See the filled tables above.}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of truth tables worksheet.