What is the value of the expression !(true && false)? What is the value of the expression false || (true && false)?
Understand the Problem
The question asks for the evaluation of two logical expressions using boolean values. The first expression involves a NOT operation applied to an AND operation between true and false, while the second expression involves an OR operation between false and (true AND false). The aim is to determine the resulting boolean values of both expressions.
Answer
First expression: true; Second expression: false.
Answer for screen readers
The value of the first expression is true, and the value of the second expression is false.
Steps to Solve
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Evaluate the first expression: ! (true && false)
First, we need to evaluate the expression inside the parentheses. The AND operation ($\land$) between true and false gives:
$$ true \land false = false $$
Now, we apply the NOT operation ($\neg$) to this result:
$$ ! (false) = true $$
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Evaluate the second expression: false || (true && false)
Again, we start with the expression inside the parentheses by evaluating the AND operation:
$$ true \land false = false $$
Now, we evaluate the OR operation ($\lor$) with false:
$$ false \lor false = false $$
The value of the first expression is true, and the value of the second expression is false.
More Information
The NOT operation inverts the boolean value, while AND and OR operations combine boolean values based on their logical definitions.
Tips
- Confusing AND with OR: Remember, AND ($\land$) results in true only if both operands are true, while OR ($\lor$) results in true if at least one operand is true.
- Not applying NOT correctly: Ensure that you apply the NOT operation to the result of the expression rather than the individual operands.
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