Relations

Fun Class Activities:

1. List all the elements (pairs) in the relation $\text{Equals}$ that is defined from $S = \{1, 2, 4, 15\}$ to $T = \{2, 5, 15, 21, 32\}$.
2. List all the elements (pairs) in the relation $\text{EvenToOdd}$, which relates even integers to odd integers, that is defined from $S = \{1, 2, 4, 15\}$ to $T = \{2, 5, 15, 21, 32\}$.
3. List all the elements (pairs) in the relation $\text{GreaterThan}$, or $>$, that is defined from $S = \{1, 2, 3, 4\}$ to $S = \{1, 2, 3, 4\}$.
4. Consider the set $S = \{$😀$,$ 😁$,$ 😎$,$ 😜$\}$ and the following relation on $S$: $R = \{(😀, 😀), (😁, 😁), (😎, 😎), (😜, 😜)\}$.
   What relation is this?

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You can create your own relations between any sets you are working with, and also create or choose a symbol for that relation, e.g., $\approx$ (

$\approx$

), $\bowtie$ (

$\bowtie$

), or even $\heartsuit$ (

$\heartsuit$

). Just make sure to clearly describe what the related sets are, and what exactly the relation is doing; that is, what is the rule by which elements are related?