(a) If A={1,2,3,4}, B={2,4,5,8}, C={3,4,5,6,7}, find (i) B ∪C, (ii) A ∩B, (iii) A-C. (b) Let S={

step 1 In this problem, we are given that in part A that set A is nothing but 1, 2, 3, 4, set B is 2, 4

(a) If A={1,2,3,4}, B={2,4,5,8}, C={3,4,5,6,7}, find (i) B...

(a) If $A=\{1,2,3,4\}, B=\{2,4,5,8\}, C=\{3,4,5,6,7\}$, find
(i) $B \cup C$,
(ii) $A \cap B$, (iii) $A-C$.
(b) Let $S=\{a, b, c, d, e\}$ be the Universal set and let $A=\{a, b, d\}$ and $B\{b, d, e\}$ be two of its subsets. Find $(A \cap B)^{\prime}$ and $(A \cup B)^{\prime}$.

Key Concepts

Complement

The complement of a set refers to all the elements in a universal set that are not in the given set. When working with complements, it is essential to have a clearly defined universal set because the complement is taken with respect to it. The complement operation is a way to extract all elements missing from a subset within the context of the universal set.

Set Difference

The difference between two sets, often expressed as A - B, is a set that contains elements that are in set A but not in set B. It essentially subtracts the elements of one set from another and is particularly useful in identifying unique elements in one set relative to another.

Set

A set is a well-defined collection of distinct objects or elements. In mathematics, sets are used to group items together and are foundational to many topics including logic, probability, and algebra. The elements in a set can be anything, from numbers to abstract objects, and the order of elements in a set is irrelevant.

Union of Sets

The union of two or more sets is a set that contains every element that appears in any of the sets. It is denoted by the symbol ?. The union operation combines the contents of the sets without repetition, meaning each element is listed only once regardless of how many sets it appears in.

Intersection of Sets

The intersection of two or more sets is a set that contains only the elements that are common to all the sets. It is denoted by the symbol ?. The intersection focuses on the shared elements among the sets, excluding those that do not appear in every set involved.

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