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  • Determine whether each of the following are reflexive,symmetric and transitive:1. Relation R in the set N of natural numbers defined as R=(x,y):y=x+5 and x <4?

Determine whether each of the following are reflexive,symmetric and transitive:1. Relation R in the set N of natural numbers defined as R=(x,y):y=x+5 and x <4?

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R=(x,y):y=x+5andx<4=(1,6),(2,7),(3,8)

(1,1) doesnot belong to R

herefore  R is not reflexive.
Also (2,7) belongs to R. 

But (7,2 ) doesnot belong to R

herefore  R is not symmetric.
Since there is no such pairs in R such that (x,y) and (y,z) belongs to R, then surely (x,z) is not possible to belong to R.
herefore  R is not transitive.
Hence, R is neither reflexive, nor symmetric, nor transitive.

Posted by

Deependra Verma

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