Questions: Define the proposition in symbols using: - p The weather is bad. - q. The trip is cancelled. - r. The trip is delayed. Proposition in words: The weather being good is a sufficient condition for the trip not to be delayed.

Define the proposition in symbols using: - p The weather is bad. - q. The trip is cancelled. - r. The trip is delayed. Proposition in words: The weather being good is a sufficient condition for the trip not to be delayed.
Transcript text: Define the proposition in symbols using: - $p$ The weather is bad. - $q$. The trip is cancelled. - $r$.The trip is delayed. Proposition in words: The weather being good is a sufficient condition for the trip not to be delayed. Proposition in symbols:
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Solution

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Solution Steps

Step 1: Understand the Proposition in Words

The proposition given in words is: "The weather being good is a sufficient condition for the trip not to be delayed."

Step 2: Translate the Proposition into Logical Statements
  • "The weather being good" is the negation of the proposition "The weather is bad," which is represented by \(\neg p\).
  • "The trip not to be delayed" is the negation of the proposition "The trip is delayed," which is represented by \(\neg r\).
Step 3: Formulate the Sufficient Condition

A statement "A is a sufficient condition for B" can be translated into a logical implication: \(A \rightarrow B\).

In this case, "The weather being good" (\(\neg p\)) is a sufficient condition for "The trip not to be delayed" (\(\neg r\)). Therefore, the logical implication is:

\[ \neg p \rightarrow \neg r \]

Final Answer

\[ \boxed{\neg p \rightarrow \neg r} \]

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