1
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-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
A
$$\left| X \right| = 1,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$
B
$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 1$$
C
$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$
D
None of the above
2
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-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
$${A \cup B}$$
B
$${{A^c} \cup {B^c}}$$
C
$${A \cap B}$$
D
$${{A^c} \cap {B^c}}$$
3
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-0.3
Which of the following statements is false?
A
The set of rational numbers is an abelian group under addition.
B
The set of integers is an abelian group under addition.
C
The set of rational numbers from an abelian group under multiplication.
D
The set of real numbers excluding zero is an abelian group under multiplication.
4
GATE CSE 1995
MCQ (Single Correct Answer)
+1
-0.3
The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is
A
$$2$$
B
$$4$$
C
$$8$$
D
None of the above
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