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."
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 $q$."
Solution
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.