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if A,B,C be three sets such that A c...

if A,B,C be three sets such that `A cup B=A cupC and Acap B=Acapc=phi,`then

A

A=B

B

B=C

C

A=C

D

A=B=C

Text Solution

Verified by Experts

we have ,
`Acup B=Acup C`
`implies (Acup B) cap C=(Acup C)cap C`
`implies (AcapC) cup (Bcap C)=C`
`implies (A capB)cup (Bcap C)=C[ :' Acap C=AcapB]. . .(i)`
Again ,
`Acup B=Acup C`
` implies (Acup B)cap B=(Acup C)capB`
`implies B=(AcapB)cup (BcapC)`
from (i) and (ii) , we get B=C.
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OBJECTIVE RD SHARMA ENGLISH-SETS-Section I - Solved Mcqs
  1. which one of the following is (A-B)cup(B-A)?

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  2. if A and B are two sets them (A-B)cup (B-A)cup (AcapB)is equal to

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  3. if A,B,C be three sets such that A cup B=A cupC and Acap B=Acapc=...

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  4. Let A and B be two sets that Acap X =Bcap X=phi and Acup X=Bcup X ...

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  5. If U be the universal set and AuuBuuC=U,"then "[(A-B)uu(B-C)uu(C-A)'] ...

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  6. The sets S and E are defined as given below: S={(x,y): |x-3|lt1and|y...

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  7. if A={(x,y):x^(2)+y^(2)le1,x,yinR]and B={(x,y):x^(2)+y^(2)le x^(2)+y...

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  8. Solve : 2 cos^(2)theta + sin theta le 2, where pi/2 le theta le (3pi)...

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  9. 20 teachers of a school either teach mathematics or physics 12 of ...

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  10. A market research group conducted a survey of 2000 consumers and re...

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  11. A college warded 38 medals in football, 15 in basketball and 20 in ...

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  12. In a class of 55 students the number of students studying subject...

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  13. If A={x,y):x^(2)+y^(2)=25} and B={(x,y):x^(2)+9y^(2)=144}, then A ...

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  14. If n(A) = 10,n(B) = 6 and n( C ) =5 for three disjoint sets A,B...

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  15. in a certain town 25% families own a cell phone 15% familesown ...

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  16. Three sets A,B and C are such that A=B nnCandB=CnnA

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  17. If A = {x , y}, then the power set of A is

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  18. the intersection of all the intervals having the form [1+(1)/(...

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  19. The value of (A cup B cup C) cap (A cap B^(C)capC^(C)) cap C^(C) is

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  20. about to only mathematics

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