sdpkjc

Answer: 1000101101

sdpkjc

Answer: 100001001

sdpkjc

To find a satisfying assignment for the given CNF formula with 10 variables and 40 clauses, we systematically analyze the clauses and assign truth values to variables to satisfy all clauses. Here's the step-by-step breakdown:

1. **Identify Key Variables**:  
   - Variable 4 appears in 18 clauses (13 positive, 5 negative). Setting it to **1 (true)** immediately satisfies 13 clauses:  
     `3,5,7,10,12,13,14,17,21,22,25,31,39`.

2. **Handle Implications of Variable 4 = 1**:  
   - Clauses where `-4` appears are now reduced. For example:  
     - Clause 27 (`-4 -7`) becomes `-7`, requiring **7 = 0 (false)**.  
     - Clause 36 (`-4 6 7`) becomes `6 ∨ 7`. Since **7 = 0**, **6 = 1 (true)** is enforced.  

sdpkjc

To find a satisfying assignment for the given CNF formula, we proceed through a systematic analysis of the clauses and variables. Here's the step-by-step reasoning:

1. **Initial Observations**: The formula has 9 variables and 36 clauses. No unit clauses or pure literals are immediately apparent, so we start by making strategic assignments based on clauses with high variable occurrence.

2. **Assigning Variable 1**: Setting `v1 = 1` simplifies many clauses. This satisfies clauses containing `1` (e.g., clauses 6, 7, 10, 12, 19, 21, 27, 29, 36) and leaves clauses with `-1` (clauses 5, 24, 34) to depend on other literals.

3. **Clause Analysis After `v1 = 1`**:
   - **Clause 2** (`5 2`): Requires `v2 = 1` or `v5 = 1`.
   - **Clause 5** (`2 -6 5 8`): With `v1 = 1`, it reduces to requiring `2`, `-6`, `5`, or `8` to be true.
   - **Clause 4** (`-5 -3 -8`): If `v5 = 0`, this clause is satisfied via `-5`.