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For a finite set A, the number of elemen...

For a finite set A, the number of elements in A is denoted by n(A). Use a Venn diagram (or otherwise) to prove that, for any two sets A,B
`n(AcupB)=n(A)+n(B)-n(AcapB)`

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CHHAYA PUBLICATION-SET THEORY -Long answer type questions
  1. For a finite set A, the number of elements in A is denoted by n(A). Us...

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  2. Given, A={x:0 lt x le2} and B={x:1 lt x lt3}, find A capB

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  3. Given, A={x:0 lt x le2} and B={x:1 lt x lt3}, find A cupB

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  4. Given, A={x:0 lt x le2} and B={x:1 lt x lt3}, find A-B

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  5. Given, A={x:0 lt x le2} and B={x:1 lt x lt3}, find (A cupB)-(AcapB)

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  6. Let A={x:2 lex lt5} and B={x: 3lt x lt 7} be two subsets of the univer...

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  7. If P={p,q,r,s,t,u} and Q capR={q,r,v,w}, find (P cup Q) cap(PcupR)

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  8. If P={p,q,r,s,t,u} and Q capR={q,r,v,w}, find (P-Q)cup(P-R)

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  9. If A,B,C be three subsets of the universal set S where S={1,2,3,4,5,...

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  10. If U={a,b,c,d,e,f} be the universal set and A,B,C are three subsets of...

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  11. If U={a,b,c,d,e,f} be the universal set and A,B,C are three subsets of...

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  12. Given X cupY={1,2,3,4} , X cup Z={2,3,4,5}, X capY={2,3} and X cap Z =...

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  13. Verify the following relations using Venn diagrams : (AcupB)cap(Acup...

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  14. Verify the following relations using Venn diagrams : Acap(B cupC)=(A...

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  15. Verify the following relations using Venn diagrams : (AcupB)^c=A^c c...

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  16. Verify the following relations using Venn diagrams : (AcapB)^c=A^c c...

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  17. Verify the following relations using Venn diagrams : A-(BcapC)=(A-B)...

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  18. Verify the following relations using Venn diagrams : A-(BcupC)=(A-B)...

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  19. Verify the following relations using Venn diagrams : (A-C)cap(B-C)=(...

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  20. Draw a Venn diagram of three non-empty sets A , B and C such that A ...

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