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FIT1058 Foundations of computing - S1 2025

FIT1058 Foundations of computing - S1 2025

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For which of the following would a sequence be a good choice of representation?

A collection of objects that appear in some room

The total cost of all items on a shopping list

A list of student names arranged so that their surnames appear in alphabetical order

A record of all the people who attended a particular party (where the order of the people is not of any particular concern)

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Which of the following statements contains a free variable?

All dragons breathe fire.

X = “smaug”

X breathes fire

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In the statement $X \le 10$ X \le 10, which of the following is an example of a variable?

$X \le 10$ X \le 10

$\le$ \le

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Suppose you have a unary function someFunction(X) and a unary predicate somePredicate(Y). Which of the following statements provides sufficient additional information to allow the nested expression someFunction(somePredicate(Y)) to be legal?

The codomain of someFunction must be {True, False}

The domain of someFunction must be {True, False}

The domain of somePredicate must be {True, False}

The codomain of somePredicate must be {True, False}

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Suppose $\text{isEven}(X)$ \text{isEven}(X) evaluates to True when X is an even number, and False otherwise. When X is assigned some numerical value, what is the value of the expression $\text{isEven}(X) \vee \text{isEven}(X+1)$ \text{isEven}(X) \vee \text{isEven}(X+1) ?

always False

False if X is even, and True otherwise

True if X is even, and False otherwise

always True

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Suppose square(X) takes an integer value as its argument, and gives its square. Which of the following is true about square(X)?

It is a function with domain $\mathbb{N}\cup\{0\}$ \mathbb{N}\cup\{0\} and codomain $\mathbb{Z}$ \mathbb{Z}.

It is a predicate with domain $\mathbb{Z}$ \mathbb{Z} and codomain $\mathbb{N}\cup\{0\}$ \mathbb{N}\cup\{0\}.

It is a predicate with domain $\mathbb{N}\cup\{0\}$ \mathbb{N}\cup\{0\} and codomain $\mathbb{Z}$ \mathbb{Z}.

It is a function with domain $\mathbb{Z}$ \mathbb{Z} and codomain $\mathbb{N}\cup\{0\}$ \mathbb{N}\cup\{0\}.

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A predicate can be described as… (Pick the statement that applies.)

A proposition whose domain is {True, False}.

A function whose codomain is {True, False}.

A function whose domain is {True, False}.

A proposition whose codomain is {True, False}.

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Which of the following is not an example of a predicate?

A function called square(Y) which gives the square of the argument value Y.

A function called isLarger(A, B) which is True if A is larger than B, and False otherwise.

A function called computer(P) which determines whether or not the argument P is a computer.

A function called isEven(X) which is True if X is even, and False otherwise.

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Suppose isPositive(X) evaluates to True when X is a positive number, and False otherwise. If X = -2, which of the following is not true about isPositive(X)?

It is a function.

It is a proposition.

It is a constant.

It is unary.

It is a predicate.

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Which of the following is an example of a ternary predicate?

A function called divisibleByThree(X) which is True if X is divisible by 3, and False otherwise.

A function called allUnique(A, B, C) which is True if the values of A, B, and C are all different, and False otherwise.

A function called divideByThree(X) which gives the value of X divided by 3.

A function called average(A, B, C) which gives the average of the numerical values A, B, and C.

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