Question

Universe U : all students in this session.

C(x) : Person x is a computer science major student.
Q(x) : Person x took Quiz 1.
G(x) : the grade of person x in Quiz 1. Choose the equivalent proposition for Each student either received a grade of 0 for Quiz 1 or took Quiz 1
A. ∃x((G(x)=0)→Q(x))
B. ∀x((G(x)=0)∨Q(x))
C. ∀x((G(x)=0)→Q(x))
D. ∃x((G(x)=0)∨Q(x))

Answer 1

The correct proposition matching the statement that each student either received a grade of 0 or took Quiz 1 is option B, written as ∀x((G(x)=0)∨Q(x)).

Step-by-step explanation:

The student is presented with a situation regarding universal statements and needs to choose the equivalent proposition. The correct answer is option B, which is ∀x((G(x)=0)∨Q(x)). This option translates to 'Every student either received a grade of 0 for Quiz 1 or took Quiz 1,' encompassing all students in the session. It is a universal affirmative statement that applies to the entire set of students attending the session, adhering to the principles of logic regarding necessity and sufficiency.