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 trueb.Both p and q are truec.Neither p nor q is trued.None of the above
Solution 1
The correct answer is b. Both p and q are true.
In logic, the compound proposition "p AND q" is true only when both p and q are true. This is the definition of the logical conjunction (AND). If either p or q is false, then the whole statement "p AND q" is false.
Solution 2
To determine when the compound proposition "p AND q" is true, we need to consider the truth values of both p and q.
If both p and q are true, then the compound proposition "p AND q" is true. This means that option b. "Both p and q are true" is a valid answer.
If either p or q is false, then the compound proposition "p AND q" is false. This means that option a. "Either p or q is true" is not correct.
If neither p nor q is true, then the compound proposition "p AND q" is also false. This means that option c. "Neither p nor q is true" is not correct.
Therefore, the correct answer is b. "Both p and q are true."
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