Question

In the following question, the domain of discourse is a set of students at a university. Define the following predicates: E(x): x is enrolled in the class T(x): x took the test Translate the following English statements into a logical expression with the same meaning.

a. Someone took the test who is enrolled in the class.
b. All students enrolled in the class took the test.
c. Everyone who took the test is enrolled in the class.
d. At least one student who is enrolled in the class did not take the test.

Answer 1

The predicates E(x) and T(x) can be defined as x is enrolled in the class and x took the test. The translations are: a. Someone took the test who is enrolled in the class. b. All students enrolled in the class took the test. c. Everyone who took the test is enrolled in the class. d. At least one student who is enrolled in the class did not take the test.

Step-by-step explanation:

In the given scenario, the predicates can be defined as follows:

• E(x): x is enrolled in the class
• T(x): x took the test

The translations of the English statements into logical expressions are:

1. a. ∃x(E(x) ∧ T(x)): Someone took the test who is enrolled in the class.
2. b. ∀x(E(x) → T(x)): All students enrolled in the class took the test.
3. c. ∀x(T(x) → E(x)): Everyone who took the test is enrolled in the class.
4. d. ∃x(E(x) ∧ ∼T(x)): At least one student who is enrolled in the class did not take the test.