Math Problem Statement
Construct a truth table for the statement.
r (r ~r)
Solution
To construct a truth table for the statement , we need to consider all possible truth values for the variable and then evaluate each part of the expression step by step.
Here's the breakdown:
- - the initial variable.
- - the negation of .
- - the disjunction (logical OR) of and .
- - the conjunction (logical AND) of and the result from step 3.
Now, let's fill in the truth table:
T | F | T | T |
F | T | T | F |
Explanation:
- Column 1 (): Lists the possible truth values of (True and False).
- Column 2 (): Lists the negation of .
- Column 3 (): This is always True because or covers all possibilities (one of them will always be true).
- Column 4 (): The result depends on . If is True, the result is True; if is False, the result is False.
Would you like to go into more detail or have any questions?
Here are five related questions you might explore next:
- What is the truth table for ?
- How does De Morgan's Law apply to logical expressions?
- Can you create a truth table for ?
- What is the difference between a tautology and a contradiction?
- How do truth tables help in understanding logical equivalences?
Tip: Practice constructing truth tables for different logical expressions to get a better grasp of how each logical operator works.
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Math Problem Analysis
Mathematical Concepts
Logic
Truth Tables
Formulas
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Theorems
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Suitable Grade Level
Grades 10-12