### Logic and Boolean Algebra Exercises1. **Simplify the following statement:**\[ [(p \rightarrow q) \lor (q \rightarrow r)] \land (r \leftrightarrow s) \]2. **a) Using a truth table, show that** \( p \lor [\neg(p \land q)] \) **is a tautology.** **b) Without using a truth table, show that the negation of the statement in (a) is a contradiction.**---**Explanation of the Problem Set:**1. The first problem involves simplifying a logical statement with implication (\(\rightarrow\)), disjunction (\(\lor\)), and biconditional (\(\leftrightarrow\)) operators. The statement combines these logical operations to form a compound expression that needs to be simplified.2. The second problem is two-part: - Part (a) requires constructing and analyzing a truth table to demonstrate that the given expression is a tautology. A tautology is a statement that is true in every possible interpretation. - Part (b) asks to prove, without using a truth table, that the negation of the given tautological statement results in a contradiction. A contradiction is a statement that is false in all possible interpretations.This exercise is designed to enhance your understanding of simplifying logical expressions and proving properties of statements using Boolean algebra and truth tables.

Name: ### Logic and Boolean Algebra Exercises1. **Simplify the following st
Uploaded: 2024-03-20T06:38:44.000Z
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Description: ### Logic and Boolean Algebra Exercises1. **Simplify the following statement:**\[ [(p \rightarrow q) \lor (q \rightarrow r)] \land (r \leftrightarrow s) \]2. **a) Using a truth table, show that** \( p \lor [\neg(p \land q)] \) **is a tautology.**