Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; `S={(m/n , p/q)"m , n , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq m = p n"}` . Then
(1) neither R nor S is an equivalence relation
(2) S is an equivalence relation but R is not an equivalence relation
(3) R and S both are equivalence relations
(4) R is an equivalence relation but S is not an equivalence relation

Explanation

To determine whether the relations R and S are equivalence relations, we need to check for three properties: reflexivity, symmetry, and transitivity.

### Step 1: Analyze Relation R
**Definition of R:**
R = {(x, y) | x, y are real numbers and x = wy for some rational number w}

**Reflexivity:**
For R to be reflexive, every element x must relate to itself.
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