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 $

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 $

Accepted Answer

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".

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) \( A + B \cdot C \)

Answer with Explanation

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) \( A + B \cdot C \)

Answer with Explanation

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) \( A + B \cdot C \)