This statement: [(p → q) ↔ (¬ p ∨ q) ] is tautologyGroup startsTrue or False
Question
This statement: [(p → q) ↔ (¬ p ∨ q)]
is tautologyGroup starts
True or False
Solution
To determine whether the statement is a tautology, we will analyze both sides using truth tables.
1. Break Down the Problem
We need to evaluate the expressions and under all possible truth values for and to check if they are equivalent for all cases.
2. Relevant Concepts
- The implication is defined as .
- A statement is a tautology if it is true for all possible truth values of the variables involved.
3. Analysis and Detail
We will construct a truth table with all possible combinations of truth values for and :
T | T | T | F | T | T |
T | F | F | F | F | T |
F | T | T | T | T | T |
F | F | T | T | T | T |
4. Verify and Summarize
Now, we analyze the last column:
- In all scenarios, the expression evaluates to True.
Final Answer
The statement is a tautology. Therefore, the answer is True.
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