1
GATE CSE 1995
Subjective
+2
-0
(a) Consider the relation scheme $$R(A, B, C)$$ with the following functional dependencies:
\eqalign{ & A,B \to C \cr & \,\,\,\,\,\,C \to A \cr}
Show that the scheme $$R$$ is the Third Normal Form $$(3NF)$$ but not in Boyce-Code Normal Form $$(BCNF).$$

(b) Determine the minimal keys of relation $$R.$$

2
GATE CSE 1995
MCQ (Single Correct Answer)
+2
-0.6
If the proposition $$\neg p \Rightarrow q$$ is true, then the truth value of the proposition $$\neg p \vee \left( {p \Rightarrow q} \right)$$ where $$'\neg '$$ is negation, $$' \vee '$$ is inclusive or and $$' \Rightarrow '$$ is implication, is
A
true
B
multiple-valued
C
false
D
cannot be determined
3
GATE CSE 1995
MCQ (Single Correct Answer)
+2
-0.6
A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is black the other is white is
A
2/3
B
4/5
C
$${\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$
D
1/3
4
GATE CSE 1995
MCQ (Single Correct Answer)
+2
-0.6
Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Then
A
A is closed under * but $$< A,\,* >$$ is not a semigroup.
B
$$< A,\,* >$$ is a semigroup but not a monoid.
C
$$< A,\,* >$$ is a monoid but not a group.
D
$$< A,\,* >$$ is a group but not an abelian group
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