How does the lack of brackets affect the proposition A ∨ B ∧ C?
Understand the Problem
The question is asking how the absence of brackets influences the logical proposition A ∨ B ∧ C, particularly regarding the order of operations and any potential ambiguity in evaluation.
Answer
A ∨ (B ∧ C)
The lack of brackets means that the AND operator takes precedence, so the expression is interpreted as A ∨ (B ∧ C).
Answer for screen readers
The lack of brackets means that the AND operator takes precedence, so the expression is interpreted as A ∨ (B ∧ C).
More Information
In logic, AND (∧) operations are performed before OR (∨) operations due to the operators' precedence rules.
Tips
A common mistake is to assume the expression is evaluated left-to-right without considering operator precedence.
Sources
- 1.1: Propositional Logic - Engineering LibreTexts - eng.libretexts.org
- Associative property - Wikipedia - en.wikipedia.org
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