1

GATE CSE 2001

MCQ (Single Correct Answer)

+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

$${R_1}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ 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?

2

GATE CSE 1999

MCQ (Single Correct Answer)

+1

-0.3

The number of binary relations on a set with $$n$$ elements is:

3

GATE CSE 1998

MCQ (Single Correct Answer)

+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?

4

GATE CSE 1998

MCQ (Single Correct Answer)

+1

-0.3

Suppose $$A$$ is a finite set with $$n$$ elements. The number of elements in the Largest equivalence relation of $$A$$ is

Questions Asked from Set Theory & Algebra (Marks 1)

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