Assignment:
Q1) Find a relation R on a set S that is neither Symmetric nor antisymmetric
Q2) Let S be a set containing exactly n elements. How many antisymmetric relations on S are there.
Q3) Give a recursive definition of X^n for any positive integer n
Q4) Give a recursive definition of the nth odd positive integer
Q5) Let g: Z -> Z be defined by g(x)= ax + b, where Z denotes the set of integers and a,b E Z with a not equal 0
a) Prove that g is one-to-one
b) What must be true about a and b if g is onto?
Q6) Let S be a set of people. For x, y E S, define xRy to mean that x = y or x is a decendant of y. Prove that R is a partial order on S.
Provide complete and step by step solution for the question and show calculations and use formulas.