Truth Tables for:1. ~ p ∧ q2. ~ p ∧ (q ∨ ~ r)3. (p∨q) ∧ ~ (p∧q)
Question
Truth Tables for:1. ~ p ∧ q2. ~ p ∧ (q ∨ ~ r)3. (p∨q) ∧ ~ (p∧q)
Solution
Sure, let's break down each of these expressions and create their truth tables.
- ~ p ∧ q
This expression is saying "not p and q". Here's the truth table:
| p | q | ~p | ~p ∧ q |
|---|---|---|---|
| T | T | F | F |
| T | F | F | F |
| F | T | T | T |
| F | F | T | F |
- ~ p ∧ (q ∨ ~ r)
This expression is saying "not p and (q or not r)". Here's the truth table:
| p | q | r | ~p | ~r | q ∨ ~r | ~p ∧ (q ∨ ~r) |
|---|---|---|---|---|---|---|
| T | T | T | F | F | T | F |
| T | T | F | F | T | T | F |
| T | F | T | F | F | F | F |
| T | F | F | F | T | T | F |
| F | T | T | T | F | T | T |
| F | T | F | T | T | T | T |
| F | F | T | T | F | F | F |
| F | F | F | T | T | T | T |
- (p∨q) ∧ ~ (p∧q)
This expression is saying "(p or q) and not (p and q)". Here's the truth table:
| p | q | p∨q | p∧q | ~(p∧q) | (p∨q) ∧ ~(p∧q) |
|---|---|---|---|---|---|
| T | T | T | T | F | F |
| T | F | T | F | T | T |
| F | T | T | F | T | T |
| F | F | F | F | T | F |
In these tables, T stands for True and F stands for False.
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