Question

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"Greater than equal to relation defined on set of integers is ...
a) Symmetric b) Partial order relation c) Equivalence relation d) not a relation
0 (a)
0 (b)
0 (c)
0 (d)​

Answer 1

The correct option is "b"

In order to show that  ≥  is a partial order, We need to prove three things:

(1) Reflexivity: For each integer  n ,  n ≥ n.  

(2) Antisymmetric: If both  n ≥ m  and  m ≥ n,  then  m=n.  

(3) Transitivity: If  n ≥ m  and  m ≥ k,  then  n ≥ k.

• Reflexivity:  For each integer  n ,  n−n  is zero or positive.

• Antisymmetric: If both  n−m  and  m−n  are each zero or positive, then  m=n.  

• Transitivity: If  n−m  and  m−k  are both zero or positive, then  n−k  is also zero or positive.

Hence Greater than equal to relation defined on set of integers is partial order relation.

Answer 2

• From the given question the correct option is b.

• In partial order relation, there is no relation between two elements.

• The partial order relation is antisymmetric and transitive.

• Greater than equal to a relation defined onset of integers is the partial order relation.

• It is also known as strict and non-strict relation. it is an irreflexive and reflexive.