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2025/WI Discrete Structures I (CS-250-01 MTH-231-01)

2025/WI Discrete Structures I (CS-250-01 MTH-231-01)

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Which of these functions are examples of partial functions? Select all that apply.

$f:\mathbb {N} \times \mathbb {N} \to \mathbb {N}$ f(x, y) = x * y

$f:\mathbb {N} \times \mathbb {N} \to \mathbb {N}$ f(x, y) = x - y

$f:\mathbb {N} \times \mathbb {N} \to \mathbb {N}$ f(x, y) = x / y

$f:\mathbb {N} \times \mathbb {N} \to \mathbb {N}$ f(x, y) = x + y

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If x = -3.8, what is $\lceil x \rceil$ ?

-3

-4

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Suppose f : A → B. What is the range of f? Select all answers that apply. Hint: There is more than one correct answer.

f(A)

{f(a) | a ∈ A}

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Which of the following are log function properties? Select all that apply.

log_b(xy) = log_bx + log_by

✅

log_b(x^y) = y(log_b(x))

✅

log_b(b^x) = x

✅

log_b(x/y) = log_bx - log_by

✅

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Which of the following statements are always true? Select all that apply.

(f ∘ g) ∘ h = f ∘ (g ∘ h)

(f ∘ g)(x) = f(g(x))

(f ∘ g)(x) = (g ∘ f)(x)

A function that always returns its argument is called an identity function.

What is gcd(12, 15)?

Evaluate dist(3,(seq(4))).

<(3,1), (3,2), (3,3), (3,4)>

<0, 3, 6, 9, 12>

<(3,0), (3,1), (3,2), (3,3), (3,4)>

<30>

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Evaluate map(ceil ∘ log₂, <2, 3, 4, 5>).

<4, 8, 16, 32>

<1, 1, 2, 2>

<2, 3, 4, 5>

<1, 2, 2, 3>

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If x = 3.8, what is $\lfloor x\rfloor$ ?

-3

-4

Consider the function f : {a, b, c} → {1, 2, 3} defined by f(a) = 1, f(b) = 1, f(c) = 2. What is f^-1({1, 3})?

{a, b, c}

{a, b}

{c}

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