Math Problem Statement
If p and q are false, what is the truth value of ¬ (p Λ q)?
Solution
To determine the truth value of the expression , we need to follow these steps:
-
Understand the components:
- and are both false ().
- is the logical "and" operator, which results in true only if both operands are true.
- is the logical "not" operator, which inverts the truth value.
-
Evaluate the expression inside the parentheses:
Since both and are false, is also false. -
Apply the negation:
Thus, the truth value of is true.
Would you like more details, or do you have any questions?
Here are 5 related questions to expand your understanding:
- What is the truth value of when both and are false?
- How does the truth table of compare with ?
- What is the truth value of if is true and is false?
- Can you explain De Morgan's laws using the given expression?
- What happens to the truth value of if is true and is false?
Tip: When working with logical expressions, it's helpful to construct truth tables to visualize how different operators affect the truth values.
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Math Problem Analysis
Mathematical Concepts
Propositional Logic
Logical Operators
Formulas
¬(p Λ q) = ¬F = T
Theorems
De Morgan's Laws
Suitable Grade Level
Grades 9-12