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make a compound propositions that is a contradiction.

To create a compound proposition that is a contradiction, we need a proposition that results in falsehood (F) in all possible truth values for \( p \) and \( q \).

A simple example of a contradiction is the compound proposition \( p \land \neg p \) (which means "p AND NOT p"). This is always false because \( p \) and \( \neg p \) cannot be true at the same time.

Let's fill in the truth table for \( p \land \neg p \):

| \( p \) | \( q \) | \( \neg p \) | \( p \land \neg p \) |
|--------|--------|--------------|----------------------|
| T      | T      | F            | F                    |
| T      | F      | F            | F                    |
| F      | T      | T            | F                    |
| F      | F      | T            | F                    |

In all cases, \( p \land \neg p \) results in \( F \), which makes it a contradiction.

Let me know if you would like more details or if you'd like to explore another concept! Here are five related questions to explore:

1. What is a tautology in propositional logic?
2. Can you provide an example of a contingency compound proposition?
3. How does the truth table of a tautology differ from a contradiction?
4. What is the role of logical connectives like \( \land \) (AND) and \( \lor \) (OR)?
5. How would the truth table look for \( p \lor \neg p \)?

**Tip:** A contradiction is a compound proposition that is always false, regardless of the truth values of its individual components.

Supply the table with necessary compound propositions to create another tautology, contradiction, and contingency propositions.

This page helps you understand how to create tautology, contradiction, and contingency propositions using truth tables. Explore key logical concepts such as tautologies, contradictions, and contingencies in propositional logic. Suitable for students in Grades 10-12.

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