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Let A,B and C be three sets. If A in B a...

Let A,B and C be three sets. If `A in B and B subC,` is it true that `A subC?` Justify your answer by an example.

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The correct Answer is:
No, because if `A={x},B={{x},y} and C={y,{x},z}` then `AinBand B subC" but "A cancelsubC`
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CHHAYA PUBLICATION-SET THEORY -Short answer type questions
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  2. Define three sets P,Q and R such that PcapQnephi,QcapR ne phi, R capP ...

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  3. Let A,B and C be three sets. If A in B and B subC, is it true that A s...

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  4. Let S={a,b,c,d,e} be the universal set and let A={a,b,d}and B={b,d,e} ...

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  5. Let S={1,2,3,4,5,6} be the universal set. Let A cupB={2,3,4}, find A^c...

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  6. If aNN={ax:x inNN}, describe 3NN cap7 NN where NN is the set of natura...

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  7. Let A,B and C be three sets. Show by means of examples that each of th...

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  8. Let A,B and C be three sets. Show by means of examples that each of th...

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  9. Let A,B and C be three sets. Show by means of examples that each of th...

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  10. For any two sets A and B, prove the following : (B-A) capA=phi

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  11. For any two sets A and B, prove the following : A^c-B^c=B-A

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  12. For any two sets A and B, prove the following : A-B=A-(AcapB)

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  13. For any two sets A and B, prove the following : A-B=AcapB'

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  14. For any two sets A and B, prove the following : B-A^c =AcapB

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  15. For any two sets A and B, prove the following : B sube(A-B)^c

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  16. For any two sets A and B, prove the following : (A cupB)-(AcapB)=(A-...

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  17. For any two sets A and B, prove the following : (A-B)cup(AcapB)=A

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  18. Let ZZ be the set of integers and A={x:x =6n, n in ZZ},B={x : x =4n,n ...

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  19. Using set operations find the H.C.F. of the numbers 12, 15 and 18.

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  20. Applying set operations find the L.C.M. of the numbers 15, 25 and 30.

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