Logic and Truth Tables worksheet - Free Printable

Sure! Let’s solve this logic tables worksheet step by step. We’ll fill in all the truth tables using standard logical operators:

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🔹 1. Negation (~p)

Negation flips the truth value:
- If `p` is T, then `~p` is F
- If `p` is F, then `~p` is T

✔ Completed table:

| p | ~p |
|---|----|
| T | F |
| F | T |

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🔹 2. Conjunction (p ∧ q)

Conjunction (AND) is true only when both p and q are true.

✔ Completed table:

| p | q | p ∧ q |
|---|---|--------|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |

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🔹 3. Disjunction (p ∨ q)

Disjunction (OR) is true if at least one of p or q is true.

✔ Completed table:

| p | q | p ∨ q |
|---|---|--------|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |

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🔹 4. Table: p, q, ~q, p ∨ ~q

We need to compute `~q` first, then `p ∨ ~q`.

Let’s go row by row:

#### Row 1: p=T, q=T → ~q=F → p ∨ ~q = T ∨ F = T
#### Row 2: p=T, q=F → ~q=T → p ∨ ~q = T ∨ T = T
#### Row 3: p=F, q=T → ~q=F → p ∨ ~q = F ∨ F = F
#### Row 4: p=F, q=F → ~q=T → p ∨ ~q = F ∨ T = T

✔ Completed table:

| p | q | ~q | p ∨ ~q |
|---|---|----|--------|
| T | T | F | T |
| T | F | T | T |
| F | T | F | F |
| F | F | T | T |

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🔹 5. Table: p, q, ~p, ~p ∨ q

Compute `~p`, then `~p ∨ q`

#### Row 1: p=T, q=T → ~p=F → F ∨ T = T
#### Row 2: p=T, q=F → ~p=F → F ∨ F = F
#### Row 3: p=F, q=T → ~p=T → T ∨ T = T
#### Row 4: p=F, q=F → ~p=T → T ∨ F = T

✔ Completed table:

| p | q | ~p | ~p ∨ q |
|---|---|----|--------|
| T | T | F | T |
| T | F | F | F |
| F | T | T | T |
| F | F | T | T |

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🔹 6. Table: p ∧ ~q

We need to compute `~q`, then `p ∧ ~q`

#### Row 1: p=T, q=T → ~q=F → T ∧ F = F
#### Row 2: p=T, q=F → ~q=T → T ∧ T = T
#### Row 3: p=F, q=T → ~q=F → F ∧ F = F
#### Row 4: p=F, q=F → ~q=T → F ∧ T = F

✔ Completed table:

| p | q | ~q | p ∧ ~q |
|---|---|----|--------|
| T | T | F | F |
| T | F | T | T |
| F | T | F | F |
| F | F | T | F |

*(Note: The header for this last table is cut off, but from context, it's clearly "p ∧ ~q".)*

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## ✔ Final Answer Summary:

Here are all completed tables:

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Negation:

| p | ~p |
|---|----|
| T | F |
| F | T |

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Conjunction:

| p | q | p ∧ q |
|---|---|--------|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |

---

Disjunction:

| p | q | p ∨ q |
|---|---|--------|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |

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p, q, ~q, p ∨ ~q:

| p | q | ~q | p ∨ ~q |
|---|---|----|--------|
| T | T | F | T |
| T | F | T | T |
| F | T | F | F |
| F | F | T | T |

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p, q, ~p, ~p ∨ q:

| p | q | ~p | ~p ∨ q |
|---|---|----|--------|
| T | T | F | T |
| T | F | F | F |
| F | T | T | T |
| F | F | T | T |

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p ∧ ~q:

| p | q | ~q | p ∧ ~q |
|---|---|----|--------|
| T | T | F | F |
| T | F | T | T |
| F | T | F | F |
| F | F | T | F |

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You can now copy these into your worksheet! Let me know if you’d like explanations of any operator or want to build more complex truth tables. 😊