MHB Demonstrating Distributive Property of Boolean Algebra

AI Thread Summary
The discussion focuses on demonstrating the distributive property of Boolean algebra through a truth table analysis. It shows that the expression p v (q ^ r) is equivalent to (p v q) ^ (p v r), while also clarifying that it is not equivalent to (p v q) ^ r. The truth table provided confirms these relationships by comparing the outputs of each expression across all variable combinations. The key property being illustrated is the distributive law of Boolean algebra. Understanding this property is essential for simplifying and manipulating Boolean expressions effectively.
barbara
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This truth table that represents statement p v (q ^ r) is equivalent to (p v q) ^ (p v r)Showing that this statement is not equivalent to (p v q) ^ r.. Now I need to what property of Boolean Algebra is being demonstrated by the fact that the first two statements were equivalentp q r q ^ r p v (q ^ r) p V q p V r (pVq) ^(pVr) (pVq) ^r
T T T T T T T T T
T T F F T T T T F
T F T F T T T T T
T F F F T T T T F
F T T T T T T T T
F T F F F T F F F
F F T F F F T F F
F F F F F F F F F
 
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