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Show that n(P(P(P( phi))))=4...

Show that `n(P(P(P( phi))))=4`

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If p - frac(1)(p) = m then let's show that (p + frac(1)(p))^2 = m^2 + 4

If A and B are two events then show that P(B) = P(A). P(B/A) + P(A^C).P(B/A^C).0 < P(A) < 1 .

If A and B are mutually exclusive events, show that P(A/(A uu B)) = frac(P(A))(P(A)+P(B))

If the coefficients of the pth , (p+1)and (p+2) terms in the expansions of (1+x)^(n) are in A.P , show that , n^(2)-n(4p+1)+4p^(2)-2=0

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

Supposing P(A cap B)>0 , show that P(B cap C|A)=P(B|A)P(C|A cap B) .

For any three events A. B.' C show that P(AcupBcupC)=P(A)+P(B)+P(C)-P(AcapB)-P(BcapC)-P(CcapA)+P(AcapBcapC)

If A and B are two mutually exclusive events and P(A cup B) ne 0 , then show that, P[A//(A cup B)] =(P(A))/(P(A)+P(B)) .

If P(A)=a and P(B)=b, Show that P(A/B) lea/b .

If P(A)=a and P(B)=b, then show that P(A/B) le(a)/(b) .

PATHFINDER-SETS AND RELATIONS-QUESTION BANK
  1. If the sets A,B are such that A cup B=B cap A thrn show that A=B

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  2. If A={1,2,3,4} nd B={2,4,6,8} then find n(A cup B)

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  3. Show that n(P(P(P( phi))))=4

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  4. If mRn={(m,n):(m-n) is divisible by 5} then find (3Rn)cap(5Rn)

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  5. If f(x)=3x-5 and x in {-1,0,1,3,4} then find the range of f

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  6. If A={x:x^2=9 and 2x=3} then find set A

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  7. For any set A,B prove that A cap (B-A)=phi

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  8. If A={2,3,5} and B={2,5,6} then (A cap B)xx(A-B)=

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  9. If A= {a,b} B={p,q} then how many relation are there from set A to set...

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  10. P={(x,y):x,y in N and 3x+2y=15} is a relation on a set of natural numb...

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  11. If B subseteqA then prove that B-A=phi

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  12. Let A={1,2,3,5} and B={4,6,9} let R =R={(x,y):abs(x-y) is odd x in A,...

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  13. Find the domain and range of the relation R={(a,b):a+b=10,a,b in N}

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  14. IfA={x:0lt xlt4} and B={x:3lexlt6} where x is an integer then show tha...

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  15. If A,B,C are three non empty sets such that A cupB=A cup C and Acap B=...

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  16. If A={1,2,3} ,B={3,4} and C={1,3,5} find Axx(BcupC)

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  17. If A and B be any two subsets of the set S then show that (AxxB) cap (...

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  18. If f:R rarr R be defined by f(x)=x^2+3 where R is the set of real numb...

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  19. Twos ets A and B are such that n(A)=3 nad n(B)=6 find the least value ...

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  20. A survey is taken of 100 boys in a village it is found that 35 boys us...

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