et X, Y , and Z be sets. (a) Construct examples for X, Y and Z so that the following conditions are true. Be sure to clearly show the validity of each condition given your example. Also, the universe here is R. i. X is open. ii. Y is open. iii. Z is closed. iv. X ⊂ Z. (b) Using your example above, derive X ∪ Y . Is this set open? Is this set closed? Explain. (c) Using your example above, derive X∪Z. Is this set open? Is this set

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A: Introduction: We know that the difference property of two sets A and B as A/B=A∩B'.

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Q: 2. Consider the following statement: "if A, B are two non-empty sets, each one having a minimum,…

A: Let, mA = min {x : x ∈ A}        mB = min {x : x ∈ B}   Now, let m = min{mA , mB} Then, m = mA if mA…

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A: given

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.