GATE CSE 2013 | Set Theory & Algebra Question 33 | Discrete Mathematics

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

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

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

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

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 2010

MCQ (Single Correct Answer)

-0.3

Consider the set $$S = \left\{ {1,\,\omega ,\,{\omega ^2}} \right\},$$ where $$\omega $$ and $${{\omega ^2}}$$, are cube roots of unity. If $$ * $$ denotes the multiplication operation, the structure $$\left\{ {S,\, * } \right\}$$ forms

a group

a ring

an integral domain

a field

GATE CSE 2010

MCQ (Single Correct Answer)

-0.3

What is the possible number of reflexive relations on a set $$5$$ elements?

2¹⁰

2¹⁵

2²⁰

2²⁵

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