Unit :1 Set Theory Prof. A.J. SHAKADWIPI. Sets and Subsets A well-defined collection of objects. finite sets, infinite sets, subset A={1,3,5,7,9} B={x|x.

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Presentation transcript:

Unit :1 Set Theory Prof. A.J. SHAKADWIPI

Sets and Subsets A well-defined collection of objects. finite sets, infinite sets, subset A={1,3,5,7,9} B={x|x is odd} C={1,3,5,7,9,...} A is a subset of B. C is a subset of B.

Null set or empty set If set contains no elements then it is known as empty set or null set. Ex. Set of positive odd nos less than 1. null set or empty set symbols {}, 

Different ways to describe the sets Listing method In this method the elements are listed within the braces. Ex A ={1,2,3,4,5} B ={ PENCIL,BOOKS,RUBBER} C={A,C,S,R,G,W}

Statement form: A statement describing the set especially where the elements having common property. eg. A set of all teachers of computer department.

Set builder notations: it specify the property shared by all elements. Eg. A={X|X>10} A is the set of all x such that x is greater than 10. Here | denotes such that

A= {X is element of odd no less than 20} X is elements of odd nos, symbolically represented as X Є odd nos >20.

Some special symbols common notations (a) Z=the set of integers={0,1,-1,2,-1,3,-3,...} (b) N=the set of nonnegative integers or natural numbers{1,2,3……..} (c) Z + =the set of positive integers{0,1,2,3……} (d) Q=the set of rational numbers (e) Q + =the set of positive rational numbers (f) Q*=the set of nonzero rational numbers (g) R=the set of real numbers (h) R + =the set of positive real numbers (i) R*=the set of nonzero real numbers (j) C=the set of complex numbers

Subset If every element of set A is also element of set B, then we say that set A is subset of B. or a contains in B. Properties: Every set is subset of itself The empty set is subset of itself

Universal set If all sets considered during a specific discussion are subset of given set, called universal set.

Equality of sets If two sets of equal A is the subset of B B is subset of A THEN A AND B are equal. A C B, B C A Eg. A ={C,COBOL,PASCAL} B={COBOL,PASCAL,C} HENCE A=B.

Venn diagrams VENN diagram is a pictorial representation of set. Venn diagram U A A A B

Universal set Arbitrary set

UNION INTERSACTION