1
GATE CSE 2015 Set 2
Numerical
+1
-0
The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$$ is _____________.
Your input ____
2
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Suppose $$𝑈$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$𝑇$$ and $$T'$$ denote the complement of $$𝑇.$$ For any $$T,R \in U,$$ let $$T\backslash R$$ be the set of all elements in $$𝑇$$ which are not in $$𝑅.$$ Which one of the following is true?
A
$$\forall X \in U\,\,$$ $$\left( {\left| X \right| = \left| {X'} \right|} \right)$$
B
$$\exists X \in U$$ $$\exists Y \in U\,\,$$ $$\left( {\left| X \right| = 5,\left| Y \right| = 5} \right.$$ and $$\left. {X \cap Y = \phi } \right)$$
C
$$\forall X \in U\,$$ $$\forall Y \in U\,\,$$ $$\,\,\left( {\left| X \right| = 2,\left| Y \right| = 3{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} and{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} X\backslash Y = \phi } \right)$$
D
$$\forall X \in U\,\,$$ $$\forall Y \in U\,\,$$ $$\,\left( {X\backslash Y = Y'\backslash X'} \right)$$
3
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Let $$X$$ and $$Y$$ be finite sets and $$f:X \to Y$$ be a function. Which one of the following statements is TRUE?
A
For any subsets $$A$$ and $$B$$ of $$X$$, $$\left| {f\left( {A \cup B} \right)} \right| = \left| {f\left( A \right)} \right| + \left| {f\left( B \right)} \right|$$
B
For any subsets $$A$$ and $$B$$ of $$X$$, $${f\left( {A \cap B} \right)}$$ $$=$$ $$f\left( A \right) \cap f\left( B \right)$$
C
For any subsets $$\left| {f\left( {A \cap B} \right)} \right| = \min \left\{ {\left| {f\left( A \right)} \right|,\left| {f\left( B \right)} \right|} \right\}$$
D
for any subsets $$S$$ and $$T$$ of $$Y$$, $${f^{ - 1}}\left( {S \cap T} \right) = {f^{ - 1}}\left( S \right) \cap {f^{ - 1}}\left( T \right)$$
4
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
A Binary operation $$ \oplus $$ on a set of integers is defined as $$x$$ $$ \oplus $$ $$y$$ $$ = {x^2} + {y^2}$$. Which one of the following statements is TRUE about $$ \oplus $$ ?
A
Commutative but not associative
B
Both commutative and associative
C
Associative but not Commutative
D
Neither commutative nor associative
GATE CSE Subjects
Software Engineering
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EXAM MAP
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NEET
Graduate Aptitude Test in Engineering
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CBSE
Class 12