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Expand the following down to their representations as sets and simplify.

i.) ⟨1, 2, 3⟩_{1}=

ii.) ⟨1, 2, 2⟩_{1}=

These are the definitions i have

Recall the deﬁntion of ordered pairs:

⟨a, b⟩ def = {{a}, {a, b}}

Recall the following expansion and simpliﬁcation from class

⟨a, a,⟩ = {{a}, {a, a}} = {{a}, {a}} = {{a}}

Using ordered pairs we could deﬁne ordered triples in two diﬀerent ways:

⟨a, b, c⟩_{1}def = ⟨a, ⟨b, c⟩⟩

⟨a, b, c⟩_{2}def = ⟨⟨a, b⟩, c⟩

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# Homework Help: Ordered triples

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