Practice: Functions · The Lumenary

Functions

Warm-upHuman

Let $A = \{1, 2, 3\}$ and $B = \{a, b\}$ . Which of these rules is a function from $A$ to $B$ ?

Choose one

1 \mapsto a,\; 2 \mapsto a,\; 3 \mapsto b

1 \mapsto a,\; 2 \mapsto b

1 \mapsto a,\; 1 \mapsto b,\; 2 \mapsto a,\; 3 \mapsto b

Functions

CoreHuman

How many functions are there from a set with $3$ elements to a set with $2$ elements?

Functions

CoreHuman

How many injective functions are there from a 2-element set to a 4-element set?

Functions

CoreHuman

Which of these functions $\Z \to \Z$ are surjective? (Choose all that apply.)

Choose all that apply

n \mapsto n + 1

n \mapsto 2n

n \mapsto -n

n \mapsto n^2

Functions

StretchHuman

A school has 400 students. Why must at least two of them share a birthday (day and month)?

Choose one

There are at most 366 possible birthdays, so the function from students to birthdays cannot be injective.Because birthdays are random.It isn't certain; it's just very likely.

Functions

StretchComputational

A finite function can be stored as a Python dictionary, e.g. {1: 'a', 2: 'b', 3: 'a'}. Write is_injective(f) returning True exactly when no two keys have the same value.

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