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Official PYQ · 2001Q2.25Tuple Calculus and SQLMCQ1 mark

GATE CS 2001 Q2.25 — Tuple Calculus and SQL

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Consider a relation geq which represents "greater than or equal to", that is, (x,y)∈(x,y) \in geq only if y≥xy \geq x.

create table geq
(	
    ib	integer	not null,
    ub	integer	not null,
    primary key ib,	
    foreign key (ub) references geq on delete cascade
);

Which of the following is possible if tuple (x,y) is deleted?

Choose one option
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Answer: C

In the relation geq, the primary key is ib and the foreign key is ub, which references ib. The relation represents the "greater than or equal to" condition, meaning for any tuple (u,v)(u, v), we must have v≥uv \geq u.

When we delete the tuple (x,y)(x, y):

  1. The primary key xx is deleted.
  2. Due to ON DELETE CASCADE, any tuple with foreign key ub =x= x must also be deleted. Let this tuple be (w,x)(w, x). Since (w,x)∈geq(w, x) \in \text{geq}, we have x≥wx \geq w. If w≠xw \neq x, then w<xw < x.
  3. Deleting the tuple (w,x)(w, x) means its primary key ww is deleted.
  4. This deletion cascades to any tuple (z,w)(z, w) whose foreign key is ww.

Since w<xw < x, the deleted tuple (z,w)(z, w) satisfies the condition w<xw < x. Therefore, it is possible that a tuple (z,w)(z, w) with w<xw < x is deleted.

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