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A simple prompt can be formally structured as a combination of two key elements: an instruction, denoted by 'c', which specifies the task, and a user input, denoted by 'z', which provides the context or data for the task.

Structural Components of a Simple Prompt

A simple prompt, denoted as $$\mathbf{x}$$, can be formally expressed as a tuple containing an instruction, $$\mathbf{c}$$, and a user input, $$\mathbf{z}$$. This relationship is mathematically represented by the formula: $$\mathbf{x} = (\mathbf{c}, \mathbf{z})$$.

Formula for a Simple Prompt

Consider the following complete text provided to a language model: 'Translate the following sentence into Spanish: 'The weather is beautiful today.'' 

Break this text down into its two primary structural components. For each component, identify the text and explain its specific role in directing the model to perform the desired task.

Deconstructing a Model's Input

A user wants a language model to translate a sentence into Spanish. They input only the following text: 'The sky is blue.' The model responds by continuing the sentence, saying: '...and the grass is green.' Based on the two key structural elements of a simple prompt, explain why the model did not perform the translation task.

Diagnosing a Flawed Prompt

Analyze the following prompt provided to a language model: 'Summarize the key points of the following text: Artificial intelligence is a branch of computer science that aims to create machines capable of intelligent behavior.' Which option correctly identifies the two primary structural components of this prompt?

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