Question

For this problem, use the predicates: F(x) is "x is a Freshman", S(x) be "x is a student at MTU", C(y) is "y is a CS course", and T(x,y) is "x is taking y", where x has the domain of all students at MTU and y has the domain of all CS courses.

(a) Translate the logical expression into English: Vx (F(x) →T(x, CS1000)).
(b) Translate English into logic: "Some freshman at MTU are taking C$1121."
(c) Translate English into logic: "Every freshman at MTU is taking a CS course."

Answer 1

The logical expression ∀x (F(x) → T(x, CS1000)) translates to 'For every student x at MTU, if x is a Freshman, then x is taking the CS1000 course.' 'Some freshmen at MTU are taking CS1121.' translates to ∃x (F(x) ∧ S(x) ∧ T(x, CS1121)). 'Every freshman at MTU is taking a CS course.' translates to ∀x (F(x) → ∃y (C(y) ∧ T(x, y))).

Step-by-step explanation:

The question involves translating logical expressions using predicates into English, and vice versa, within the context of students and courses at a university.

Part (a): Translation of Logical Expression into English:

The logical expression ∀x (F(x) → T(x, CS1000)) translates to "For every student x at MTU, if x is a Freshman, then x is taking the CS1000 course".

Part (b): Translation from English into Logic:

"Some freshman at MTU is taking CS1121." can be translated into logic as ∃x (F(x) ∧ S(x) ∧ T(x, CS1121)), where ∃ denotes 'there exists' and ∧ denotes 'and'.

Part (c): Translation from English into Logic:

"Every freshman at MTU is taking a CS course." translates to the logical expression ∀x (F(x) → ∃y (C(y) ∧ T(x, y))), where ∀ denotes 'for all', → denotes 'implies', ∃ denotes 'there exists', and ∧ denotes 'and'.