Let A={2,3}, B={4,5}, C={2,3,{4,5}}. (a) Which of the following are true? (i) A ∈C, (ii) B ∈

step 1 in this problem we have given that set A is sub B is that C is 2 3 this is an example of a withi

Let A={2,3}, B={4,5}, C={2,3,{4,5}}. (a) Which of the...

Let $A=\{2,3\}, \quad B=\{4,5\}, \quad C=\{2,3,\{4,5\}\}$.
(a) Which of the following are true?
(i) $A \in C$,
(ii) $B \in C$,
(iii) $C-A=B$
(b) Also find the following sets:
$A \cup B, \quad B \cup C, \quad A \cap C, \quad B \cap C$

Key Concepts

Set Intersection

The intersection of two sets is the set containing the elements that are common to both sets, denoted by ?. This concept is key in determining the shared characteristics of sets and is used to extract the common elements from multiple sets.

Set Union

The union of two sets is the set containing all the elements that are in either set, denoted by ?. It collects the elements from both sets without repetition. This operation is fundamental for combining the contents of sets while maintaining the properties of set theory.

Set Difference

Set difference is the operation that results in the set of elements that are in one set but not in another, commonly denoted by a minus sign. For instance, for sets X and Y, the difference X - Y includes all elements of X that are not present in Y. This operation is useful for excluding certain elements from a set.

Set Membership

Set membership is the fundamental concept in set theory that distinguishes whether an object is an element of a set. It is denoted by the symbol ?, meaning that if x ? S, then x is one of the members of the set S. This concept is essential for understanding statements like whether one set is an element of another set.

Element Versus Subset

It is important to differentiate between an element of a set and a subset of a set. An element is an individual object contained within a set, whereas a subset is a set whose all elements belong to another set. For instance, while a particular set might appear as an element within another set, this does not automatically mean that it behaves like a subset in operations such as unions, intersections, or set differences.

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