Notes and Worksheet on Sets

Notes and Worksheet on Sets - Math 100 Talking about sets...

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Math 100 Talking about sets Martin H. Weissman 1. Examples of sentences about sets Let S = { 2 , 5 , { 2 } , { 3 , 4 }} . The following are true sentences about S , involving the phrase “is an element of”: (1) 2 is an element of S . Symbolically, 2 S . (2) 5 is an element of S . Symbolically, 5 S . (3) { 2 } is an element of S . Symbolically, { 2 } ∈ S . (4) { 3 , 4 } is an element of S . Symbolically, { 3 , 4 } ∈ S . (5) 3 is not an element of S . Symbolically, 3 6∈ S . (6) { 2 , 5 } is not an element of S . Symbolically, { 2 , 5 } 6∈ S . The following are true sentences, involving counting elements of S . (1) There are four elements of S . Symbolically, # S = 4. (2) There are two elements of S , which are numbers. There is not a nice way of saying this symbolically. (3) There is one element of S , which is an even number. There is not a nice way of saying this symboli- cally. The following are true sentences, involving the phrase “is a subset of”: (1) The empty set is a subset of S . Symbolically, ∅ ⊂ S . (2)
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Notes and Worksheet on Sets - Math 100 Talking about sets...

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