GATE CSE 1998 | Set Theory & Algebra Question 82 | Discrete Mathematics

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GATE CSE 1998

MCQ (Single Correct Answer)

-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?

both assertions are true

assertion
(i) is true but assertion (ii) is not true

assertion
(ii) is true but assertion (i) is not true

neither (i) nor (ii) is true

GATE CSE 1997

MCQ (Single Correct Answer)

-0.3

The number of equivalence relations on the set $$\left\{ {1,2,3,4} \right\}$$ is

$$15$$

$$16$$

$$24$$

$$4$$

GATE CSE 1996

MCQ (Single Correct Answer)

-0.3

Let $$A$$ and $$B$$ be sets and let $${A^c}$$ and $${B^c}$$ denote the complements of the sets $$A$$ and $$B$$. The set $$\left( {A - B} \right) \cup \left( {B - A} \right) \cup \left( {A \cap B} \right)$$ is equal to

$${A \cup B}$$

$${{A^c} \cup {B^c}}$$

$${A \cap B}$$

$${{A^c} \cap {B^c}}$$

GATE CSE 1996

MCQ (Single Correct Answer)

-0.3

Suppose $$X$$ and $$Y$$ are sets and $$\left| X \right|$$ and $$\left| Y \right|$$ are their respective cardinalities. It is given that there are exactly 97 functions from $$X$$ to $$Y$$. From this one can conclude that

$$\left| X \right| = 1,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$

$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 1$$

$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$

None of the above

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