1
GATE CSE 1998
Subjective
+2
-0
Suppose A = {a, b, c, d} and $${\Pi _1}$$ is the following partition of A

$${\Pi _1}\, = \,\{ \{ a,\,\,b,\,\,c\,\} \,,\,\{ d\} \,\}$$
(a) List the ordered pairs of the equivalence relations induced by $${\Pi _1}$$
(b) Draw the graph of the above equivalence relation.

2
GATE CSE 1998
+1
-0.3
The number of functions from an $$m$$ element set to an $$n$$ element set is
A
$$m + n$$
B
$${m^n}$$
C
$${n^m}$$
D
$$m * n$$
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
$$n + 1$$
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