Home / Questions / Consider the following simple propositions: \( A \): It is raining. \( B \): Wind is blowing. \( C \): I am not driving. From these, create the following compound proportions: (i) \( A \lor B \)    (ii) \( \sim B \)    (iii) \( \sim A \cdot C \)    (iv) \( A \cdot \sim C \)    (v) \( A + B \cdot C \)
Explanatory Question

Consider the following simple propositions:

  • \( A \): It is raining.
  • \( B \): Wind is blowing.
  • \( C \): I am not driving.

From these, create the following compound proportions:

(i) \( A \lor B \)    (ii) \( \sim B \)    (iii) \( \sim A \cdot C \)    (iv) \( A \cdot \sim C \)    (v) \( A + B \cdot C \)

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Answer with Explanation

Using the logical connectives for OR (\( \lor \) or \( + \)), NOT (\( \sim \)), and AND (\( \cdot \)), the compound proportions are as follows:

  • (i) \( A \lor B \): It is raining OR wind is blowing.
  • (ii) \( \sim B \): Wind is NOT blowing.
  • (iii) \( \sim A \cdot C \): It is NOT raining AND I am not driving.
  • (iv) \( A \cdot \sim C \): It is raining AND I am driving.
  • (v) \( A + B \cdot C \): It is raining OR wind is blowing AND I am not driving.

Note: In part (iv), since \( C \) represents "I am not driving," its negation \( \sim C \) translates to "I am driving".