Math Problem Statement
Construct a truth table for (p ∨ q) ∨ (~p ∨ ~r). Use T for true and F for false.
Solution
The expression you provided is:
where:
- and represent statements,
- is the logical OR,
- is the logical NOT.
We'll construct a truth table for this expression. Since there are three variables , , and , the truth table will have rows, covering all possible truth values for , , and .
Here is the step-by-step breakdown:
- Compute .
- Compute .
- Compute .
- Compute .
- Finally, compute the full expression .
Let me now construct the full truth table.
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Math Problem Analysis
Mathematical Concepts
Logic
Truth Table
Propositional Logic
Formulas
Logical OR ( ∨ )
Logical NOT ( ~ )
Theorems
De Morgan's Laws
Basic Truth Table Construction
Suitable Grade Level
Grades 9-12