1.
We have relation:
It is equivalence relation.
Reflexivity: since and , then
Symmetry: since , then and
Transitivity: if and then .
Since we have and
Partition is:
, where
2.
a) Relation "less than" on the set N is not equivalence relation:
No reflexivity: a number cannot be less than itself.
No symmetry: if then
Transitivity: if and then
b) Relation "has the same shape as" on the set of all triangles is equivalence relation:
Reflexivity: one triangle has single shape
Symmetry: two triangles can have same shape
Transitivity: three triangles can have same shape
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