To express \( A \lor B \) (logical "or") in terms of implication \( \Rightarrow \) alone, we can use the fact that \( A \lor B \) can be rewritten using De Morgan's law and implications.

### Steps:

1. Recall that \( A \lor B \) is logically equivalent to \( \neg A \Rightarrow B \). This can be proven using truth tables.
   
2. Here's the explanation:
   - If \( A \lor B \) is true, it means either \( A \) is true, \( B \) is true, or both are true.
   - Another way of stating this is that if \( A \) is false, then \( B \) must be true, which gives us \( \neg A \Rightarrow B \).

Thus, the expression for \( A \lor B \) using only implication is:
\[
A \lor B \equiv \neg A \Rightarrow B
\]

This formula uses only the implication operator \( \Rightarrow \).

Would you like any further details or a deeper breakdown?

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Here are 5 related questions:
1. How do you prove the equivalence between \( A \lor B \) and \( \neg A \Rightarrow B \) using a truth table?
2. How would you express \( A \land B \) using only \( \Rightarrow \)?
3. How can other logical operators, like \( \neg \), be expressed in terms of \( \Rightarrow \)?
4. What is the formal definition of the material implication \( A \Rightarrow B \)?
5. Can you express exclusive "or" (XOR) using only \( \Rightarrow \)?

**Tip:** In logic, many operations can be reduced to simpler ones, like implication, helping to simplify more complex logical systems.

Learn how to express the logical disjunction A ∨ B using only implication (⇒). This solution involves key concepts in propositional logic, including De Morgan's Law and material implication. Suitable for undergraduate-level students studying logic or discrete mathematics.

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