Sets - Properties

Rarely Tested

A is a subset of B if and only if all elements of  A are already present in B

  • The set of all subsets of a set A is called the power set of A

  • The null set is a subset of all sets

  • Every set is a subset of itself
  • If A=B, A $$\subset$$ B and B $$\subset$$ A

  • A $$\cup$$ (B$$\cup$$C) = (A $$\cup$$ B)$$\cup$$C
  • A $$\cap$$ (B$$\cap$$C) = (A $$\cap$$ B)$$\cap$$C
  • A $$\cup$$ (B$$\cap$$C) = (A $$\cup$$ B)$$\cap$$( A $$\cup$$ C)
  • A $$\cap$$ (B$$\cup$$C) = (A $$\cap$$ B)$$\cup$$( A $$\cap$$ C)
  • A $$\cup$$ Ø = A
Question 1

The number of non empty subsets of the set A={0,1,2,3,4} is?

Question 2

ABX India ltd has 50 employees, each of whom speak at least one language out of English, Hindi and Marathi. The Venn diagram below gives the number of people speaking each language. If there are 20 people who can speak Hindi and 12 who can speak Marathi, how many employees can speak only in English?

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Other Venn Diagrams Formulas


3 Set Venn Diagram


2 Set Venn Diagram

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