The relation SS defined on the set of real numbers by the rule aSb , if a⩾b is an:

# The relation SS defined on the set of real numbers by the rule aSb , if a⩾b is an:

1. A
An equivalence relation
2. B
Reflexive, transitive but not symmetric
3. C
Symmetric, transitive but not reflexive
4. D
Neither transitive nor reflexive but symmetric

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### Solution:

Let a be any real number,
Then we can always write a≥a. that is, aSa .
Thus, relation S is a reflexive relation over set R.
Let a,b,c be three real numbers such that, aSb and bSc,
aSb implies a≥b and bSc implies b≥c.
So, we can definitely write, a≥c and thus aSc.
So, Relation S is transitive.
Let a,b be any two real numbers such that aSb,
aSb implies a≥b,but we can't necessarily write b≥a
So, Relation S is not symmetric.
Reflexive, transitive but not symmetric.
Hence, option 2 is correct.

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