To analyze the compound proposition "p AND q", we have the following insights:

1. **Understanding the Logical Operator**: The "AND" operator in logic denotes that both conditions involved must be true for the entire proposition to be deemed true.

2. **Truth Table Representation**:
- Let $ p $ and $ q $ be propositions that can either be true (T) or false (F).
- The truth table for $ p $ AND $ q $ is as follows:

| p | q | p AND q |
|-------|-------|---------|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |

From this table, we can see that "p AND q" is true only when both $ p $ and $ q $ are true.

### Final Answer
The correct answer is: **b. Both p and q are true**.

Question

To analyze the compound proposition "p AND q", we have the following insights:

1. **Understanding the Logical Operator**: The "AND" operator in logic denotes that both conditions involved must be true for the entire proposition to be deemed true.

2. **Truth Table Representation**:
   - Let $ p $ and $ q $ be propositions that can either be true (T) or false (F).
   - The truth table for $ p $ AND $ q $ is as follows:

| p     | q     | p AND q |
   |-------|-------|---------|
   | T     | T     | T       |
   | T     | F     | F       |
   | F     | T     | F       |
   | F     | F     | F       |

From this table, we can see that "p AND q" is true only when both $ p $ and $ q $ are true.

### Final Answer
The correct answer is: **b. Both p and q are true**.

Knowee AI · Accepted Answer

To analyze the compound proposition "p AND q", we have the following insights:

1. **Understanding the Logical Operator**: The "AND" operator in logic denotes that both conditions involved must be true for the entire proposition to be deemed true.

2. **Truth Table Representation**:
   - Let $ p $ and $ q $ be propositions that can either be true (T) or false (F).
   - The truth table for $ p $ AND $ q $ is as follows:

| p     | q     | p AND q |
   |-------|-------|---------|
   | T     | T     | T       |
   | T     | F     | F       |
   | F     | T     | F       |
   | F     | F     | F       |

From this table, we can see that "p AND q" is true only when both $ p $ and $ q $ are true.

### Final Answer
The correct answer is: **b. Both p and q are true**.

The compound proposition "p AND q" is true only when:a.Either p or q is trueb.Both p and q are truec.Neither p nor q is trued.None of the above

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