Question

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 1

True:
- The conjunction p ∧ q can be stated as “the car is blue and 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.

False:
- The conjunction p ∧ q can be stated as “if the car is blue, then it is spacious.” (That is p → q, an implication, not a conjunction.)
- p is the hypothesis. (“Hypothesis” refers to the antecedent of a conditional; p here is just a propositional statement.)