GATE CSE 2015 Set 2 | Set Theory & Algebra Question 26 | Discrete Mathematics

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Let $$𝑅$$ be the relation on the set of positive integers such that $$aRb$$ if and only if $$𝑎 $$ and $$𝑏$$ are distinct and have a common divisor other than $$1.$$ Which one of the following statements about $$𝑅$$ is true?

$$𝑅$$ is symmetric and reflexive but not transitive

$$𝑅$$ is reflexive but not symmetric and not transitive

$$𝑅$$ is transitive but not reflexive and not symmetric

$$𝑅$$ is symmetric but not reflexive and not transitive

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

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which one of the following functions is continuous at $$x = 3$$?

$$f\left( x \right) = \left\{ {\matrix{ {2,} & {if} & {x = 3} \cr {x - 1} & {if} & {x > 3} \cr {{{x + 3} \over 3},} & {if} & {x < 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {4,} & {if} & {x = 3} \cr {8 - x} & {if} & {x \ne 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {x + 3,} & {if} & {x \le 3} \cr {x - 4} & {if} & {x > 3} \cr } } \right.$$

$$f\left( x \right) = \matrix{ {{1 \over {{x^3} - 27}},} & {if} & {x \ne 3} \cr } $$

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