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

Question

The compound proposition `p AND q` is true only when:

a. Either p or q is true
b. Both p and q are true
c. Neither p nor q is true
d. None of the above

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Solution

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

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.
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.

This problem has been solved

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