Hykilpikonna
93 lines
3.1 KiB
TeX
Executable File
93 lines
3.1 KiB
TeX
Executable File
% Copyright and Usage Information
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% ===============================
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% This file is provided solely for the personal and private use of students
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% taking CSC110 at the University of Toronto St. George campus. All forms of
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% distribution of this code, whether as given or with any changes, are
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% expressly prohibited. For more information on copyright for CSC110 materials,
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% please consult our Course Syllabus.
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% This file is Copyright (c) 2021 Mario Badr and Tom Fairgrieve.
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\documentclass{article}
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\setlength{\parindent}{0pt}
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\setlength{\parskip}{5pt}
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\usepackage[margin=1in]{geometry}
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\title{CSC110 Fall 2021: Term Test 1, Question 2 (Predicate Logic)}
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\author{Azalea Gui}
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\date{Wednesday October 20, 2021}
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\begin{document}
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\maketitle
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Let $A$ be the set of all animals and all plants.
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Suppose we define the following predicates:
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\begin{itemize}
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\item $Plant(x):$ ``$x$ is a plant", where $x \in A$.
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\item $Omnivore(x):$ ``$x$ is an omnivore", where $x \in A$.
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\item $Herbivore(x):$ ``$x$ is a herbivore", where $x \in A$.
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\item $IsColourful(x):$ ``$x$ is colourful", where $x \in A$.
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\item $Eats(x, y):$ ``$x$ eats $y$", where $x, y \in A$.
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\end{itemize}
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(An omnivore is an animal that eats food of both plant and animal origin.
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A herbivore is an animal that only eats plants.)
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For parts (1) to (3), translate each of the following statements from English into symbolic predicate logic.
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In part (4), you will translate an English statement into Python code.
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No explanation is necessary.
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Do not define any of your own predicates or sets.
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Use parentheses to indicate how you want to group logical expressions with multiple operators (especially when dealing with $\Rightarrow$ and $\Leftrightarrow$).
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\begin{enumerate}
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\item
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At least one plant is colourful.
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\textbf{Solution}:
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$\exists x \in A$ s.t. $Plant(x) \land IsColourful(x)$
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\item
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Omnivores eat any animal or plant.
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\textbf{Solution}:
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$\forall x, y \in A$, $Omnivore(x) \Rightarrow Eats(x, y)$
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\item
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At least one herbivore does not eat colourful plants.
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\textbf{Solution}:
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$\exists x \in A$, $\forall y \in A$, $Herbivore(x) \land ((IsColorful(y) \land Plant(y)) \Rightarrow \neg Eats(x, y))$
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\item
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Suppose we define the following in Python:
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\begin{itemize}
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\item A variable \texttt{animals\_and\_plants} which represents a set of animals and plants.
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\item Functions \texttt{is\_herbivore} and \texttt{eats} that take in argument values from \texttt{animals\_and\_plants}, and correspond to the predicates $Herbivore$ and $Eats$, respectively, defined at the top of this question.
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\item A variable \texttt{brussel\_sprouts} that refers to the plant brussel sprouts. (Note: \texttt{brussel\_sprouts in animals\_and\_plants} is True)
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\end{itemize}
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Using these definitions, translate the following statement into a Python expression:
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\begin{quote}
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All herbivores eat brussel sprouts.
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\end{quote}
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You must use a comprehension in your solution, and may not use any loops.
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\begin{verbatim}
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all([eats(x, brussel_sprouts) for x in animals_and_plants if is_herbivore(x)])
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\end{verbatim}
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\begin{center}
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\textbf{SUBMIT THIS FILE AND THE GENERATED PDF q2.pdf FOR GRADING}
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\end{center}
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\end{enumerate}
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\end{document}
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