GATE CSE 2015 Set 2 | Set Theory & Algebra Question 27 | Discrete Mathematics

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GATE CSE 2015 Set 2

Numerical

-0

The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$$ is _____________.

Your input ____

GATE CSE 2015 Set 1

MCQ (Single Correct Answer)

-0.3

For a set A, the power set of A is denoted by 2^A. If A = {5, {6}, {7}}, which of the following options are TRUE?

I. $$\phi \in {2^A}$$
II. $$\phi \subseteq {2^A}$$
III. $$\left\{ {5,\left\{ 6 \right\}} \right\} \in {2^A}$$
IV. $$\left\{ {5,\left\{ 6 \right\}} \right\} \subseteq {2^A}$$

I and III only

II and III only

I, II and III only

I, II and IV only

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-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?

For any subsets $$A$$ and $$B$$ of $$X$$, $$\left| {f\left( {A \cup B} \right)} \right| = \left| {f\left( A \right)} \right| + \left| {f\left( B \right)} \right|$$

For any subsets $$A$$ and $$B$$ of $$X$$, $${f\left( {A \cap B} \right)}$$ $$=$$ $$f\left( A \right) \cap f\left( B \right)$$

For any subsets $$\left| {f\left( {A \cap B} \right)} \right| = \min \left\{ {\left| {f\left( A \right)} \right|,\left| {f\left( B \right)} \right|} \right\}$$

for any subsets $$S$$ and $$T$$ of $$Y$$, $${f^{ - 1}}\left( {S \cap T} \right) = {f^{ - 1}}\left( S \right) \cap {f^{ - 1}}\left( T \right)$$

GATE CSE 2013

MCQ (Single Correct Answer)

-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 $$ \oplus $$ ?

Commutative but not associative

Both commutative and associative

Associative but not Commutative

Neither commutative nor associative

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