Prove that on the set of integers, the relation R defined as aRb if and only if a=±b is an equivalence relation

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Solution

1). aRa
a=+a and -a=-a
Therefore R is reflexive.

2). aRb implies bRa
a=+-b implies b=+-a
Therefore R is symmetric.

3). aRb and bRc implies aRc
a=+-b and b=+- c implies a=+-c
Therefore R is transitive.

R is an equivalence relation.

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Prove that on the set of integers, the relation R defined as aRb if and only if a=±b is an equivalence relation

1). aRa a=+a and -a=-a Therefore R is reflexive. 2). aRb implies bRa a=+-b implies b=+-a Therefore R is symmetric. 3). aRb and bRc implies aRc a=+-b and b=+- c implies a=+-c Therefore R is transitive. R is an equivalence relation.

1). aRa
a=+a and -a=-a
Therefore R is reflexive.

2). aRb implies bRa
a=+-b implies b=+-a
Therefore R is symmetric.

3). aRb and bRc implies aRc
a=+-b and b=+- c implies a=+-c
Therefore R is transitive.

R is an equivalence relation.