1
GATE CSE 2001
+1
-0.3
Consider the following relations:
$${R_1}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is even over the set of integers
$${R_2}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is odd over the set of integers
$${R_3}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,a.b > 0$$ over the set of non-zero rational numbers
$${R_4}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left| {a - b} \right| \le 2$$ over the set of natural numbers

Which of the following statements is correct?

A
$${R_1}$$ and $${R_2}$$ are equivalence relations, $${R_3}$$ and $${R_4}$$ are not
B
$${R_1}$$ and $${R_3}$$ are equivalence relations, $${R_2}$$ and $${R_4}$$ are not
C
$${R_1}$$ and $${R_4}$$ are equivalence relations, $${R_2}$$ $${R_3}$$ are not
D
$${R_1}$$, $${R_2}$$, $${R_3}$$ and $${R_4}$$ are all equivalence relations
2
GATE CSE 1999
+1
-0.3
The number of binary relations on a set with $$n$$ elements is:
A
$${n^2}$$
B
$${2^n}$$
C
$$2{n^2}$$
D
None of the above
3
GATE CSE 1998
+1
-0.3
Let $${R_1}$$ and $${R_2}$$ be two equivalence relations on a set. Consider the following assertions:

(i)$$\,\,\,\,{R_1} \cup {R_2}$$ is an euivalence relation
(ii)$$\,\,\,\,{R_1} \cap {R_2}$$ is an equivalence relation

Which of the following is correct?

A
both assertions are true
B
assertion
(i) is true but assertion (ii) is not true
C
assertion
(ii) is true but assertion (i) is not true
D
neither (i) nor (ii) is true
4
GATE CSE 1998
+1
-0.3
Suppose $$A$$ is a finite set with $$n$$ elements. The number of elements in the Largest equivalence relation of $$A$$ is
A
$$n$$
B
$${n^2}$$
C
$$1$$
D
$$n + 1$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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