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FIT1058 Foundations of computing - S1 2025

FIT1058 Foundations of computing - S1 2025

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Which of the following statements is true about functions?

A function must specify exactly one value for each argument.

A function must specify either one or zero values for each argument.

A function must specify a different value for each argument.

A function must specify one or more values for each argument.

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Suppose $A = \{0, 1\}$ A = \{0, 1\}. Which of the following statements is NOT true?

A^* is an infinite set.

For any

k > 0, the set

A^k contains twice as many strings as the set $A^{k-1}$ A^{k-1}.

For any

k > 0, the set

A^k contains the

k-digit binary representations of all numbers from

0 to $2^{k-1}$ 2^{k-1}.

The set

A^1 is a distinctly different set from

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Suppose

A is some alphabet. How many elements are in the set

A^0?

One

✅

Zero

❌

It contains infinite elements.

❌

It depends on the size of A.

❌

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Suppose $A = \{0,1,2\}$ A = \{0,1,2\}. What is the size of

Infinite

Which of the following is NOT a valid way of representing the set $\{1, 2, 3, 4, 5\}$ \{1, 2, 3, 4, 5\} ?

$(1, 5)_\mathbb{Z}$ (1, 5)_\mathbb{Z}

$[1, 6)_\mathbb{Z}$ [1, 6)_\mathbb{Z}

$(0, 6)_\mathbb{Z}$ (0, 6)_\mathbb{Z}

$[1, 5]_\mathbb{Z}$ [1, 5]_\mathbb{Z}

❌

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When working with sets of numbers, the symbol $\mathbb{N}_0$ \mathbb{N}_0 represents the same set as which of the following?

$\mathbb{Z}$ \mathbb{Z}

$\mathbb{Z}^-_0$ \mathbb{Z}^-_0

$\mathbb{Z}^-$ \mathbb{Z}^-

$\mathbb{Z}^+_0$ \mathbb{Z}^+_0

$\mathbb{Z}^+$ \mathbb{Z}^+

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Which of the following is the best alternative description of the set $\{ x \in \mathbb{R} : 0 < x < 10 \}$ \{ x \in \mathbb{R} : 0 < x < 10 \}

{1, 2, 3, 4, 5, 6, 7, 8, 9}

Select the set with the highest cardinality.

{}

{10¹⁰⁰, 10⁹⁹, 10⁹⁸, 10⁹⁷}

{supercalifragilisticexpialidocious}

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

{"really", "high", "cardinality"}

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Which of the following collections of items is not a set?

{}

{😀,😛,😎,😁,😆}

{1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64}

{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}

{1, 1, 2, 3, 5, 8, 13}

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Suppose you have written out the set of prime factors of the number 30 in ascending order, and would like to represent these values as a set. Which of the following is NOT a valid formal representation of this set of values?

$\{3, 5, 2\}$ \{3, 5, 2\}

All of the above are valid

$\{2, 3, 5\}$ \{2, 3, 5\}

$\{n : n \text{ is a prime factor of } 30\}$ \{n : n \text{ is a prime factor of } 30\}

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