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Building a portfolio website

Margin issue LaTeX fancy header

Advanced Formal Modelling Excercise-1

Let Rz={(a,b)|a,b is belongs to Z^+ and a-b is an odd positive integer}.

The set of integers is represented by the letter Z. An integer is any number in the infinite set,

Z={.., -3,-2,-1, 0, 1, 2 ,3, …}
Z+ is the set of all positive integers(1,2,3,….) there is no 0 here
Z- is the set of all negative integers (…,-3,-2,-1) there is no 0 here
Z^nonneg is the set of all positive integers including 0, while Z^nonpos is the set of all negative integers including 0


Set R1 is reflexive because
Q1) For every a is belongs to Z+ . (a,a) is belongs to R . a-a = 0 is not an odd  number. So, R is not reflexive.

For every a,b is belongs to Z+ : if a,b is positive, then b-a is negative. That if( a,b) is belongs R then (b,a) is not belongs to R. So not symmetric.

Due to the same reason, as above, (a,b) and (b,a) cannot be simultaneously in R . So the condition in the definition of anti symmetry is false.

The implication holds trivially , R is anti symmetric.

4 steps to master a new technology

My own java project step by step

Address of variable saved in stack
And the main variable or value saved in heap

Stack works with FIFO
Heap works with LIFO