Home
Class 12
MATHS
An integer m is said to be related to...

An integer `m` is said to be related to another integer `n` if `m` is a multiple of `n` . Check if the relation is symmetric, reflexive and transitive.

Text Solution

Verified by Experts

Here, `R = {(m,n):a,b in Z and m` is a multiple of `n}`
For all `a in R`,
`=> a` will be multiple of `a`.
`:. (a,a) in R`.So, `R` is refexive.

Since in `R` for every `(a,b) in R`
`=> a` is a multiple of `b`.> ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|449 Videos

  • SCALAR OR DOT PRODUCT

    RD SHARMA ENGLISH|Exercise All Questions|233 Videos

Similar Questions

Explore conceptually related problems

Give an example of a relation which is symmetric but neither reflexive nor transitive.

Give an example of a relation which is reflexive and symmetric but not transitive.

Give an example of a relation which is reflexive and transitive but not symmetric.

Consider the relation perpendicular on a set of lines in a plane. Show that this relation is symmetric and neither reflexive and nor transitive

Give an example of a relation which is symmetric and transitive but not reflexive.

Every relation which is symmetric and transitive is also reflexive.

Let R be a relation on the set of integers given by a R b :-a=2^kdotb for some integer kdot Then R is:- (a) An equivalence relation (b) Reflexive but not symmetric (c). Reflexive and transitive but not symmetric (d). Reflexive and symmetric but not transitive

Let R be a relation on the set of integers given by a R b => a=2^kdotb for some integer kdot then R is An equivalence relation Reflexive but not symmetric Reflexive and transitive but nut symmetric Reflexive and symmetric but not transitive

Let L be the set of all straight lines in the Euclidean plane. Two lines l_(1) and l_(2) are said to be related by the relation R iff l_(1) is parallel to l_(2) . Then, check the relation is reflexive , symmetric or transitive

m is said to be related to n if m and n are integers and m-n is divisible by 13. Does this define an equivalence relation?

Home
Profile