**Q. 1.** Let A = {1,2,3,4} find the number of relations on A containing (1, 2) and (3, 2) which is reflexive transitive but not symmetric giving sufficient reasons.

**Q. 2.** Let R be the set of real numbers on ‘R’ defined by R = {(a,b) / | a-b | <>

**Q. 3.**

- R= { (a,b): |a-b| is even} Find whether the relation R on A is equivalence.
- All the elements of {1,3,5} is not related to any element of {2,4} with respect to R. True/False . Justify your answer.

**Q. 4.** Let Q be the set of all rational numbers on R be the relation on Q defined by R = { (x,y) : 1 + xy > 0} Find whether relation is equivalence.

**Q. 5.** f : z -> z f(x) = x^{2} + x. rove that the function is neither injective nor subjective.

**Q. 6.** Let where f(x) = x2 – x+ 1.Prove that f is invertible and hence find f ^{-1}.

**Q. 7.** Let f: N --> Y be a function defined by f(x) = x^{2} + 1 Show that f is one – one and replace Y by a set so that f is invertible. Also find its inverse function.

**Q. 8.** Let f : R -> R g: R -> R defined by

- f(x)=x
^{2}+ 8 g(x)=3x^{3}+ 1 - f(x)=x
^{2}+ 2x – 3 g(x) = 3x – 4 Show that fog and gof exists and hence find them.

**Q. 9.**Let N be the set of all natural numbers. R be the relation on N X N defined by (a,b) R (c,d) iff ad = bc Show that R is equivalence.

**Q. 10.**

**Q. 11.**

Is the function one-one onto

**Q. 12.** A function f over the set of real numbers is defined as Find whether the function is one-one or onto