**2.** 5

**3.** 252

**4.** (i) No (ii) No (iii) Yes (iv) boundary of a unit circle and the relation *C* is called **Circle Relation**.

**5.** 2^{36}, 2^{6}(*Hint:* Number of elements in *X* × *X* is 36 and therefore number of possible subsets is 2^{36}. There are 6 elements of the form
(*a*, *a*) and so the number of reflexive relations is 2^{6}.)

**7.** The relation is not anti-symmetric

**8.** *R* = {(1, 1), (2, 2), (3, 3), (4, 4)}

**9.**

**10.**

**11.**

**12.** (i), since ...

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