Ka hoe ngā waka, ā, ka tae ki Puke-āhua i runga tata mai o te huinga o Waipā ki te awa o Waikato (NIT 1995:243). / The canoes paddled along and reached Puke-āhua, just above the confluence of the Waipā and Waikato rivers.

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Mēnā ka whakakotahi mai ngā huānga o ētahi huinga e rua, ka kīia tērā ko te huinga tūhono. Ko te ∪ hei tohu i te huinga tūhono. Hei tauira: A = {1, 2, 3, 4, 5} E = {3, 4, 5, 6, 7} A ∪ E = {1, 2, 3, 4, 5, 6, 7} (TRP 2010:128). / If the elements of two sets are combined that is called a union of sets. For example: A = {1, 2, 3, 4, 5} E = {3, 4, 5, 6, 7} A ∪ E = {1, 2, 3, 4, 5, 6, 7}.

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Ka whakamahia he hoahoa huinga hei whakaatu i te hononga kei waenganui i ētahi huinga (TRP 2010:127). / A Venn diagram is used to show the relationship amongst sets.

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Mēnā kei roto ngā huānga katoa o tētahi huinga i tētahi huinga nui ake, ka kīia he huinga iti tētahi, he huinga nui tētahi. Ko te ⊂ hei tohu i te huinga iti, ko te ⊃ hei tohu i te huinga nui. Hei tauira: A = {1, 2, 3} E = {1, 2, 3, 4, 5, 6, 7, 8} Hei huinga iti te A ki te E (A ⊂ E). Hei huinga nui te E ki te A (E ⊃ A) (TRP 2010:128). / If all the elements are in a larger set, it is called a subset and the other is a superset. The symbol ⊂ is for a subset, the symbol ⊃ s for a superset. For example: A = {1, 2, 3} E = {1, 2, 3, 4, 5, 6, 7, 8} where A to E (A ⊂ E) is a subset. E to A (E ⊃ A) is a superset.

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Mēnā kei roto ngā huānga katoa o tētahi huinga i tētahi huinga nui ake, ka kīia he huinga iti tētahi, he huinga nui tētahi. Ko te ⊂ hei tohu i te huinga iti, ko te ⊃ hei tohu i te huinga nui. Hei tauira: A = {1, 2, 3} E = {1, 2, 3, 4, 5, 6, 7, 8} Hei huinga iti te A ki te E (A ⊂ E). Hei huinga nui te E ki te A (E ⊃ A) (TRP 2010:128). / If all the elements are in a larger set, it is called a subset and the other is a superset. The symbol ⊂ is for a subset, the symbol ⊃ s for a superset. For example: A = {1, 2, 3} E = {1, 2, 3, 4, 5, 6, 7, 8} where A to E (A ⊂ E) is a subset. E to A (E ⊃ A) is a superset.

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Ko te {2, 4} te huinga pātahi o te A me te E. Ko te ∩ hei tohu i te huinga pātahi. Arā, A ∩E = {2, 4} (TRP 2010:127). / {2, 4} is the intersecting set of A and E. ∩ is the symbol for an intersecting set. That is, A ∩E = {2, 4}.

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He huinga raraunga tēnei, ko te tapeke hahao pōro a Hīria i ētahi kēmu hahau pōro e iwa {85, 82, 03, 88, 80, 78, 79, 94, 87} (TRP 2010:227). / This is a dataset, Hīria's golf score from nine golf rounds {85, 82, 03, 88, 80, 78, 79, 94, 87}.

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Karekau he hononga o te huinga A me te E, ka kīia he huinga ritua: A = {1, 3, 5, 7} E = {2, 4, 6, 8} (TRP 2010:127). / When there's no relationship between sets A and E, it is called disjoint sets.

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Mēnā karekau he huānga kei roto i tētahi huinga, ka kīia taua huinga he huinga wātea. Koia nei ngā tohu e rua: { }, Ø (TRP 2010:128). / If there are no elements in a set, that set is called an empty set. These are the two symbols: { }, Ø.

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Ina whakamahia te hangarau koiora hei whakarerekē i te huinga ira i te karihi o te pūtau, ka kīia tēnei he raweke ira. / When biotechnology is used to alter the genome in the nucleus of the cell, this is called genetic engineering.

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