ME test series doubt

Question

Consider the relation r₁(P, Q, R) and r₂(R, U, V) with primary keys R and U respectively. The relation r₁ contains 1500 tupples and r₂contains 2000 tupples. The maximum size of the join  is:

my ans is 1500 but given ans is 2000. please correct me if 1500 is not the ans.

Comments

Consider this for relatively small number of tuples:

P	Q	R
a	A	1
a	B	2
b	A	3

R	U	V
1	w	p
1	x	p
1	y	q
1	z	r

Here, join will have 4 tuples (tuples for which R=1)

So, in this scenario it will have 2000 tuples.

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Understand the difference between this question & https://gateoverflow.in/3553/gate2006-it-14

P	Q	R
1	a	A
2	a	A
3	b	A

R	S	T
A	x	q
B	x	q
C	y	s
D	z	r

Here, join will have max 3 tuples.

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I have explained both the cases above

It's the difference between which attribute you select for the key & the number of tuples in each relation.

In the second case here, they have just modified the first case by decreasing the tuples in second relation and increasing the tuples in first relation.

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thank i got it , i miss  key part in both the Q ,

Answer 1

2000 is correct ans because R in relation r1 is primary key so

R have different values bt in r2 R is not primary key so it may have all same values so join will have 2000 tupples

Comments

https://gateoverflow.in/3553/gate2006-it-14

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if the primary Key condition is reversed among tables i mean primary key of R2 is R but not R1 then what would be answer ?

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Then ans will be 1500