Write 'T' for True and 'F' for False.
`p vv (q ^^ r) -= (p vv q) ^^ (p vv r)` is an associative law.

Answer

To determine whether the statement \( p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) \) is an associative law, we need to analyze the expression step by step.

### Step 1: Understand the Operators
The expression involves two logical operators:
- \( \lor \) (disjunction, or)
- \( \land \) (conjunction, and)

### Step 2: Identify the Structure of the Expression
The left-hand side of the expression is \( p \lor (q \land r) \). This means that \( p \) is true if either \( p \) is true or both \( q \) and \( r \) are true.

The right-hand side is \( (p \lor q) \land (p \lor r) \). This means that both \( p \lor q \) and \( p \lor r \) must be true for the entire expression to be true.

### Step 3: Apply the Distributive Law
The expression \( p \lor (q \land r) \) can be analyzed using the distributive law of logic, which states that:
\[ p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) \]
This indicates that the left-hand side is actually equivalent to the right-hand side.

### Step 4: Associative vs. Distributive Law
However, the question asks if this is an associative law. Associative laws refer to the grouping of operations, such as:
- \( (a \lor b) \lor c \equiv a \lor (b \lor c) \)
- \( (a \land b) \land c \equiv a \land (b \land c) \)

Since the expression we are examining is not about grouping but about distributing, it does not fit the definition of an associative law.

### Conclusion
Since the given expression is a result of the distributive law and not the associative law, the statement is false.

Thus, the answer is:
**F** (False)

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