Q. 565.0( 1 Vote )

# State True or False for the statementsAn integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

False

Let R be the relation defined on Z by mRn if m is a integral multiple of n.

Let mRm R

m is a integral multiple of m.

Which is true since m is integral multiple of itself.

Thus, R is reflexive.

Let mRn R

m is a integral multiple of n

m= zn z Z

Since,

n is not integral multiple of m.

nRm R

Thus, R is not symmetric.

Let mRn R and nRp R

m is a integral multiple of n and n is a integral multiple of p

m is a integral multiple of p

mRp R

Thus, R is transitive.

Hence, the given statement is false.

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