(a) State whether the following statements are false or true, explain youranswer: i. Given any integers a, b, c and any positive integern \text { If } a \equiv b(\bmod n) \text { and } b \equiv c(\bmod n), \text { then } a \equiv c(\bmod n) ii. Suppose a = b(modn) and c = d(mod n),then a +c=b+c(modn). \text { iii. } 7 x \equiv 12(\bmod 7) \text {. } ) Find the least positive value of x such that: 71 \equiv x(\bmod 8) (c) Calculate the multiplicative inverse of 168 in modulo 83. (d) Calculate the inverse of 4 modulo 15. Show your steps.

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