Lisa says, 'If I don’t study, then I will not pass the test.' If p: 'I study' and q: 'I pass the test,' which symbolic statement represents Lisa's statement?
Understand the Problem
The question asks for the symbolic representation of Lisa's statement that if she doesn’t study, she will not pass the test. It involves understanding logical implications and how to express them symbolically.
Answer
The correct symbolic statement is: $\neg p \rightarrow \neg q$.
Answer for screen readers
The correct symbolic statement representing Lisa's statement is:
$$ \neg p \rightarrow \neg q $$
Steps to Solve
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Identify the statements
Let $p$ be "I study" and $q$ be "I pass the test". -
Translate Lisa's statement
Lisa says, "If I don’t study, then I will not pass the test." In symbolic terms, "not studying" is represented by $\neg p$ and "not passing the test" is represented by $\neg q$. -
Formulate the implication
The logical implication represented by Lisa's statement is: If she does not study ($\neg p$), then she will not pass the test ($\neg q$). This can be expressed as:
$$ \neg p \rightarrow \neg q $$ -
Select the correct option
Given the options, option (a) $\neg p \rightarrow \neg q$ correctly represents Lisa's statement.
The correct symbolic statement representing Lisa's statement is:
$$ \neg p \rightarrow \neg q $$
More Information
This type of logical implication is common in reasoning and proofs. It's useful to understand how to translate verbal statements into symbolic logic for clearer interpretation.
Tips
- Misinterpreting the "if-then" structure and forgetting to negate the appropriate statements.
- Confusing the symbols and their meanings, such as mixing up $p$ and $\neg p$.
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