Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN: 9781133382119

Author: Swokowski

Publisher: Cengage

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How to show that |Z+| (that is, the cardinality of Z+) is not equal to |(0,1)| (cardinality of the open interval (0,1) )?

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let S = { 1, 2, 3, 4, 5, 6}
How many subsets are there of cardinality 4?
how many subsets of cardinality 4 have {2, 3, 5} as a subset
how many subsets of cardinality 4 contain at least one odd number
how many subset of cardinality 4 contain exactly one even number

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Let S={1,2,3,4,5,6,7}
How many subsets are there of cardinality 5?
(Note: you can enter “C(n,k)” for (nk).(nk).)
How many subsets of cardinality 5 have {2,3,5} as a subset?
How many subsets of cardinality 5 contain at least one odd number?
How many subsets of cardinality 5 contain exactly one even number?

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Please help me prove this. Use an element argument to prove those. Assume that all sets are subsets of a universal set U. Please write down the definition in the step too so I can understand it. Thanks.

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I am confused on how to actually find the cardinal number when given an infinite set.Find the cardinal number of each of the following sets. Assume the pattern of elements continues in each part in the order given.{ 201, 202, 203, ..., 1100}

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How do I prove this? I found some proofs on other websites but non of them were easy to understand. Could you please include easiest possible explanation with some examples if possible?
The set of all finite subsets of a countable set is countable.

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Let X be a set and P(X) its power set. Explain what it means that the cardinality of P(X) is strictly larger than the cardinality of X, and prove it.

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CAN someone please do this asap? PLEASE SHOW ALL STEPS PLEASE PLEASEEEEEEEEEE
Use the definition of two sets have the same cardinality to prove that interval (0,2] has the same cardinality as the interval [1, +∞)

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Prove. Power set of a null set is empty.

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