The statement "p OR (NOT p)" is an example of a:a.Tautologyb.Contradictionc.Contingencyd.None of the above
Question
The statement "p OR (NOT p)" is an example of a:a.Tautologyb.Contradictionc.Contingencyd.None of the above
Solution 1
Step 1: Analyze the statement "p OR (NOT p)".
Step 2: Break down the statement into its components. In this case, we have "p" and "(NOT p)".
Step 3: Evaluate the truth values of each component. The truth value of "p" can be either true or false, while the truth value of "(NOT p)" is the opposite of "p". So, if "p" is true, then "(NOT p)" is false, and vice versa.
Step 4: Combine the truth values using the OR operator. The OR operator returns true if at least one of the components is true. So, if "p" is true, the statement "p OR (NOT p)" is true. Similarly, if "p" is false, the statement is also true.
Step 5: Determine the nature of the statement. Since the statement "p OR (NOT p)" is always true, regardless of the truth value of "p", it is an example of a tautology.
Step 6: Answer the question. The statement "p OR (NOT p)" is an example of a tautology.
Solution 2
The statement "p OR (NOT p)" is an example of a Tautology.
Here's why:
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A tautology in logic is a compound statement that is always true, no matter what the truth value of the individual statements are.
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The statement "p OR (NOT p)" is saying either p is true, or p is not true.
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No matter what truth value p has, either p will be true, or not p will be true.
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Therefore, the statement "p OR (NOT p)" is always true, making it a tautology.
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