1
GATE CSE 2006
+1
-0.3
Let $$X,. Y, Z$$ be sets of sizes $$x, y$$ and $$z$$ respectively. Let $$W = X x Y$$ and $$E$$ be the set of all subjects of $$W$$. The number of functions from $$Z$$ to $$E$$ is
A
$${2^{{2^{xy}}}}$$
B
$$2 \times {2^{xy}}$$
C
$${2^{{2^{x + y}}}}$$
D
$${2^{xyz}}$$
2
GATE CSE 2006
+1
-0.3
The set $$\left\{ {1,\,\,2,\,\,3,\,\,5,\,\,7,\,\,8,\,\,9} \right\}$$ under multiplication modulo 10 is not a group. Given below are four plausible reasons.

Which one of them is false?

A
It is not closed
B
2 does not have an inverse
C
3 does not have an inverse
D
8 does not have an inverse
3
GATE CSE 2006
+1
-0.3
For the set $$N$$ of natural numbers and a binary operation $$f:N \times N \to N$$, an element $$z \in N$$ is called an identity for $$f$$ if $$f\left( {a,z} \right) = a = f\left( {z,a} \right)$$ for all $$a \in N$$. Which of the following binary operations have an identify?
$${\rm I}$$) $$\,\,\,\,\,\,f\left( {x,y} \right) = x + y - 3$$
$${\rm I}{\rm I}$$ $$\,\,\,\,\,\,f\left( {x,y} \right) = {\mkern 1mu} \max \left( {x,y} \right)$$
$${\rm I}{\rm I}{\rm I}$$$$\,\,\,\,\,f\left( {x,y} \right) = \,{x^y}$$
A
$${\rm I}$$ and $${\rm I}$$$${\rm I}$$ only
B
$${\rm I}$$$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ only
C
$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ only
D
None of them
4
GATE CSE 2005
+1
-0.3
Let $$A$$, $$B$$ and $$C$$ be non-empty sets and let $$X = (A - B) - C$$ and $$Y = (A - C) - (B - C)$$

Which one of the following is TRUE?

A
$$X = Y$$
B
$$X \subset Y$$
C
$$Y \subset X$$
D
None of these
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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