If X, Y and Z are three sets such that X ⊃Y ⊃Z, then (X ∪Y ∪Z)-(X ∩Y ∩Z)= (1) X-Y (2) Y-Z (3) X-

step 1 Hello students in this problem set x y and z are three sets given and x is super set of y is sup

If X, Y and Z are three sets such that X ⊃Y ⊃Z, then (X ∪Y...

If $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ are three sets such that $\mathrm{X} \supset \mathrm{Y} \supset \mathrm{Z}$, then $(\mathrm{X} \cup \mathrm{Y} \cup \mathrm{Z})-(\mathrm{X} \cap \mathrm{Y} \cap \mathrm{Z})=$ (1) $\mathrm{X}-\mathrm{Y}$ (2) $\mathrm{Y}-\mathrm{Z}$ (3) $\mathrm{X}-\mathrm{Z}$ (4) None of these

If $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ are three sets such that $\mathrm{X} \supset \mathrm{Y} \supset \mathrm{Z}$, then $(\mathrm{X} \cup \mathrm{Y} \cup \mathrm{Z})-(\mathrm{X} \cap \mathrm{Y} \cap \mathrm{Z})=$
(1) $\mathrm{X}-\mathrm{Y}$
(2) $\mathrm{Y}-\mathrm{Z}$
(3) $\mathrm{X}-\mathrm{Z}$
(4) None of these

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Key Concepts

Set Union

The set union of two or more sets is the collection of all elements that belong to at least one of those sets. It is a fundamental operation in set theory that combines all elements without repeating any, and it is typically denoted by the symbol ?.

Set Intersection

The set intersection of two or more sets consists of all elements that are common to every one of the sets. This operation is crucial in set theory for determining the shared elements between sets and is represented by the symbol ?.

Set Difference

Set difference is an operation that results in a set containing the elements of one set that are not present in another. It is a method for excluding elements and is symbolically denoted by a minus sign (?).

Subset Relations and Nested Sets

Subset relations describe a situation where every element of one set is also an element of another set. When sets are nested so that one set is entirely contained within another (e.g., A ? B ? C), calculating operations like union, intersection, and difference often becomes simpler due to the predictable containment relationships.

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