CBSE Class 12-science Answered

2nd sum plz

Asked by lovemaan5500 | 08 Mar, 2020, 10:18: PM

Expert Answer

Question:-

Check whether the relation R₁ in R defined by R₁={(a, b) : a less than or equal to b3} is reflexive, symmetric or transitive. Is it an equivalence relation?

Solution:-

R space i s space a space s e t space o f space r e a l space n u m b e r s R subscript 1 equals left curly bracket left parenthesis a comma space b right parenthesis space colon thin space a less or equal than b cubed right curly bracket space i s space d e f i n e d space i n space R rightwards double arrow a space a n d space b space a r e space r e a l space n u m b e r s left parenthesis i right parenthesis F o r space x element of R space I f space x greater or equal than 0 comma space x less or equal than x cubed B u t space i f space x less than 0 comma space t h e n space x greater or equal than x cubed therefore space R subscript 1 space i s space n o t space r e f l e x i v e left parenthesis i i right parenthesis N o w comma space f o r space a comma b element of R subscript 1 a less or equal than b cubed B u t space i t space i s space n o t space n e c e s s a r y space t h a t space b less or equal than a cubed F o r space e x a m p l e colon space I f space left parenthesis 2 comma space 9 right parenthesis element of R subscript 1 comma space 2 less or equal than 9 cubed equals 729 space b u t space 9 greater than 2 cubed equals 8 therefore space R subscript 1 space i s space n o t space s y m m e t r i c left parenthesis i i i right parenthesis L e t space left parenthesis a comma space b right parenthesis comma space left parenthesis b comma space c right parenthesis element of R subscript 1 rightwards double arrow a less or equal than b cubed space space a n d space space b less or equal than c cubed T h i s space d o e s space n o t space i m p l y space t h a t space a less or equal than c cubed F o r space e x a m p l e comma space a equals 3 comma space b equals 3 over 2 comma c equals 4 over 3 3 less or equal than 3 cubed over 2 cubed equals 3.375 comma space b less or equal than 4 cubed over 3 cubed B u t comma space 3 greater than 4 cubed over 3 cubed equals 2.3 H e n c e comma space R subscript 1 space i s space n e i t h e r space r e f l e x i v e comma space s y m m e t r i c space o r space t r a n s i t i v e.

Answered by Renu Varma | 09 Mar, 2020, 11:54: AM

CBSE Class 12-science Answered

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Introduction to Relations

Concept of relations and types of relation

Introduction To Relations

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CBSE Class 12-science Answered

Concept Videos

Introduction to Relations

Concept of relations and types of relation

Introduction To Relations

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