Questions: Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. p^q can be translated as "p but q." Choose the correct answer below. A. The statement is false. p ∧ q can be translated as "p is necessary for q." B. The statement is false. p ∧ q can be translated as "p is sufficient for q." C. The statement is true. D. The statement is false. p ∨ q can be translated as "p but q."

Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. p^q can be translated as "p but q." Choose the correct answer below. A. The statement is false. p ∧ q can be translated as "p is necessary for q." B. The statement is false. p ∧ q can be translated as "p is sufficient for q." C. The statement is true. D. The statement is false. p ∨ q can be translated as "p but q."
Transcript text: Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. p^q can be translated as "p but q." Choose the correct answer below. A. The statement is false. $p \wedge q$ can be translated as " $p$ is necessary for $q$." B. The statement is false. $p \wedge q$ can be translated as " $p$ is sufficient for $q$." C. The statement is true. D. The statement is false. $p \vee q$ can be translated as "p but $q$."
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Solution

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Solution Steps

Step 1: Identify the Logical Connective and Understand its Meaning

The logical connective involved is ∧, which means Conjunction (and).

Explanation: True if both p and q are true.
Step 2: Apply the Correct Interpretation

Given the statements p: True and q: True, and using the logical connective '∧', the truth value of the statement is True.

Final Answer:

The statement is True under the logical connective: Conjunction (and). True if both p and q are true.

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