1
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
2
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
$$n + 1$$
3
GATE CSE 1998
+1
-0.3
Consider the following set a equations
x + 2y = 5
4x + 8y = 12
3x + 6y + 3z = 15 This set
A
has a unique solution
B
has no solutions
C
has finite number of solutions
D
has infinite number of solutions
4
GATE CSE 1998
+2
-0.6
In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada where as 13 persons speak both Kannada and English. How many people speak all three languages?
A
9
B
8
C
7
D
6
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