Set Operations and Important Laws Data Science and A.I. Lecture Series Set Operations Union Definition: \[ A \cup B = \{x : x \in A \text{ or } x \in B\} \] Examples: \( A = \{1, 2, 3\}, B = \{3, 4, 5\} \implies A \cup B = \{1, 2, 3, 4, 5\} […]
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Introduction to Sets and Type of Sets Data Science and A.I. Lecture Series Introduction A set is a well-defined collection of distinct objects. Examples of collections: Books in a library. Natural numbers that are factors of a given number. States in a country. Sets are fundamental in mathematics and are used in many areas,
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Example-1- Write the solution set of the equation x2+x-2=0. Solution- x2-x+2x-2=0 x(x-1)+ 2(x-1)=0 (x-1)(x+2)=0 x=1 , x= – 2 S={1, -2} Example-2- Write the set {x: x is a positive integer and x2<40} Solution- S={1, 2, 3, 4, 5, 6} 7, 8, 9, 10, ………… can not be included because their squares are greater than
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In real life, we often come across collection of objects viz. #Cricket Team #Pack of Cards #Members of a Club In mathematics, we also come across collections, examples are. #Odd natural numbers #Even natural numbers #Numbers which is divisible by 3 and less than 20. If you observe each example is well-defined collection of objects.
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