The statement "Proof of p^(qvr) <=> (p^q)v(p^r)" is an equivalence in propositional logic, which means that the two statements on either side of the symbol <=> are logically equivalent. In other words, the truth value of one statement is always the same as the truth value of the other statement.
The purpose of proving this equivalence is to show that the two statements are interchangeable. This can be useful in simplifying complex logical expressions or solving logic problems.
In order to prove this equivalence, you can use logical equivalences and rules of inference to manipulate the expressions on either side of the <=> symbol until they are equivalent to each other.
One example of how this equivalence can be used is in proving the distributive property of logical disjunction. By setting p to "It is raining", q to "I have an umbrella", and r to "I have a raincoat", we can show that the statement "If it is raining and I have an umbrella or I have a raincoat, then I am prepared for the rain" is equivalent to "If it is raining and I have an umbrella, or if it is raining and I have a raincoat, then I am prepared for the rain."
Yes, this equivalence has applications in computer science, particularly in the design and analysis of logical circuits and algorithms. It is also used in artificial intelligence and natural language processing to simplify and manipulate logical expressions.