Translating a sentence into connectives

Statement

Translate into logical connectives the sentence: “To pass the exam you must have done the assignment and handed it in”.

Solution

Let us introduce the propositions: $S$ = “I pass the exam”, $C$ = “I have done the assignment”, $G$ = “I have handed the assignment in”.

“Must” indicates a necessary condition: passing the exam implies having done both things. Hence $\boxed{S\Rightarrow(C\land G)}.$ Equivalently, by contraposition: if I have not done it or I have not handed it in, then I do not pass the exam.

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Topics: Set theory
Concepts: Logical connectives · Implication
Skills: Modelling
Exercise type: Word problem