(a) Suppose R is a relation on a set X. Define what it means to say that R is transitive. (b) Decide whether each of the following relations is transitive. [No justification is required - just write "yes" or "no" for each case.] (i) The relation R on Z defined by aRb if a + b + 1. (ii) The relation R on Z defined by aRb if a² = b². (iii) The relation R on Zx Z defined by (a, b)R(c, d) if ad = bc. (c) Let z be the complex number 4-3i. Find the following. [You do not need to show your working, but doing so may help you to gain marks if you make arithmetic errors.] (iv) z². (v) A complex number w such that wz = z.

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A: Let M=ℕ. Define relation T on M as, T=a,b : a≠ b Clearly a,a∉T for any a∈M. Hence T is irreflexive.

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