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**patman231231** **Problem 1**

Consider the following relation r on the set **Z**: (x,y) belongs to r if and only if x+y is an even number. Find if this relation is

a) Reflexive Answer:

b) Symmetric Answer:

c) Transitive Answer:

d) Equivalence relation Answer:

Problem 2 Consider the following sets:

X_{1} = Mat_{n}(**Z**), X_{2}=**Z**^{15} , X_{3} =**Z**_{15}, X_{4} = Cartesian product of **R** and **Z**

Which of the following sets has the same cardinality as cardinality of **N?**

**Problem 3**Calculate 2^{-1} + 3^{-1} in **Z**_{5}

Problem 4Present truth table for the function f(x,y) = (x + y)’x’ + y’

**Problem 5** Using truth table prove that xy +x = x