Let p represent the statement "the car is blue” and q represent the statement "the car is spacious.” What is true of the conjunction p ∧ q? Check all that apply.The conjunction p ∧ q can be stated as “the car is blue and spacious.”The conjunction p ∧ q can be stated as “if the car is blue, then it is spacious.”The statement “the car is blue and spacious” is a compound statement.The statement “the car is spacious and blue” can be written symbolically as q ∧ p.p is the hypothesis.
Answer
A
The conjunction p ∧ q can be stated as “the car is blue and spacious.”
B
The conjunction p ∧ q can be stated as “if the car is blue, then it is spacious.”
C
The statement “the car is blue and spacious” is a compound statement.
D
The statement “the car is spacious and blue” can be written symbolically as q ∧ p.
E
p is the hypothesis.
Explanation
A conjunction joins two statements with “and,” so p ∧ q means “the car is blue and spacious” (A). Because it combines the statements p and q, “the car is blue and spacious” is a compound statement (C). The order of statements in a conjunction can be reversed, so q ∧ p means “the car is spacious and blue” (D). Choice B describes a conditional, and p is not a hypothesis here because no conditional is stated.
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