candidate key

Question

Q1)  R(A1,A2,A3,..................An)  having A1A2 as its candidate key. Find the no of super key..?

Q2)   R(A1,A2,A3,..................An)  having A1 and A2 as its candidate key. Find the no of super key..?

Answer 1

(1) CK = A₁A₂

_{Every Super Key should include candidate key.Remaining attribute = n-2}

Every attribute have 2 choices.

Hence,Number of Super key=2^n-2

(2) Ck = A₁ and A₂

Number of super keys = Number of Keys because of A₁ +  Number of Keys because of A₂ -  Number of Keys because of A1 and A₂

Number of super keys = 2^n-1 + 2^n-1- 2^n-2

Answer 2

1) total superkeys ---> 2^(n-2)

2) n(A+B)= n(A) + n(B) - n(AB)

So total superkeys --> 2^(n-1) + 2^(n-1) - 2^(n-2) 

Answer 3

Q1. IN R A1A2 ARE THE CANDIDATE KEY.AND NON KEYS ARE(N-2)

SO NUMBER OF SUPERKEYS =2^(n-2)

Q2 .A1 =CANDIDATE KEY=(N-1) KEYS ARE NON KEYS THESE ARE=A2,A3,A4,A5....AN=>SUPERKEY=2^(N-1)

                                                                                                       SIMILARLY FOR A2=SUPERKEYS =2^(N-1)

NOW COMMON ELEMENT IN SET A1 AND A2 IS={A3,A4,A5,A6......AN}=(n-2)keys=THESE ARE THE KEYS WHICH COMBINED WITH BOTH {A1 AND A2} SO REMOVE THIS

==> NUM OF SUPERKEYS=2^(n-1)+2^(n-1)-2^(n-2)

IS THE ANS

YOU CAN PUT IN ANY NUM OF  SET TO VERIFIY

    

Comments

minimal means possible minimum if A1 alone is not c.key then A1A2 combination will give c.key which is minimal

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ohhh... ok... f9..thankk u..

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yes what sanjay told is correct @dhaairya

Answer 4

We know , number of super keys 2^{no of attribute- size of candidate key}

1) Number of super keys =2^n-2

2) Number of Super keys =2^n-1

Comments

For (2) your answer is not right.There are Two candidate keys is given A₁ and A₂. For only one Key your answer is right.

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case 2) in case n=3 ans should be 6 (A1,A2,A1A2,A1A3,A1A2A3,A2A3) but 2^3-1=4

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is A1A2 a super key  ??

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yes,A₁A₂ is a super Key.