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OPERATIONS ON SETS

(1) Union of Sets: The union of two sets A and B is the set of all the elements which are either in A or in B or in both A and B. It is denoted by $$A\cup B$$. Let $$\text{A}=\left\{ 1,\,\,2,\,\,\,3 \right\}$$ $$\text{B}=\left\{ 2,\,\,\,4,\,\,6 \right\}$$ $$\displaystyle \therefore \text{A}\cup \text{B}=\left\{ 1,\,\,2,\,\,3,\,\,4,\,\,6 \right\}$$ (2) Intersection of […]

VENN DIAGRAM

The pictorial representation of sets is called Venn diagram. The universal set is represented by a rectangular region and its subsets by circles inside the rectangle. In the above given Venn diagram, $$\text{B}\subseteq \text{A}\,$$and $$\text{A}\subseteq U$$ and $$\text{B}\,\subseteq \,U$$.   Here,$$\text{A}\subset U$$and $$\text{B}\subseteq U$$. If, there is no common elements in A and B and […]

SUBSETS

SUBSET: A set P is said to be a subset of a set Q if each element of P is also an element of Q. If P is subset of Q, we write $$\text{P}\subseteq \text{Q}$$ PROPER SUBSET: If $$\text{P}\subseteq \,\text{Q}$$ and $$\text{P}\ne \text{Q}$$ then P is called a proper subset of Q and we write […]

EQUIVALENT AND EQUAL SETS

EQUIVALENT SETS Two finite sets A and B are equivalent only when number of elements of both the sets are equal. Example: A = {x : x is a natural number less than 6} B = {x : x is a vowel of English alphabet} n(A) = n(B) = 5 C = {2, 4, 6, […]

SETS : DEFINITION

The word ‘set’ in mathematics was first used by a German mathematician George Cantor (1845 – 1918). A set is a well-defined collection of objects. Well – defined means universal truth. The elements do not varies person to person. Set is denoted by capital letters of English alphabets. E.g. A, B, C, D, F, G, […]