Let R be a relation on the set of all real numbers, where (x, y) E R if and only if a -y is an integer,To show that R is anti-symmetric, we must prove which of the following statement?O For any real numbers a and y, if a -For any real numbers a and y, if a # y, then ay is an integer, then ya is an integerFor any real numbers a and y, if z # y, then aO For any real numbers r andO For any real numbers a and y, if a + y, then zy is an integer andy is an integer or yy is not an integer and ya is an integerr is an integera is not an integera is not an integerIf a #y, then zy is not an integer or yTo show that Ris not anti-symmetric, we must find a counterexample satisfies which of the following statement?O For some real numbers r and y, zO For some real numbers z and y, r#y and r - y is an integer and yFor some real numbers r and y, r # y and a -For some real numbers z and y, r #y and z -For some real numbers r and y, x # y and ay is an integer, and yr is not an integery is an integer or yy is not an integer and yy is not an integer or yr is an integerI is an integerr is not an integerI is not an integer

2) Given, Let R be the relation on the set of all real numbers defined where(x,y)ER if and only if…

Let R be a relation on the set of all real numbers, where (x, y) E Rif and only if a y is an integer, To show that R is anti-symmetric, we must prove which of the following statement? O For any real numbers z and y, if z O For any real numbers z and y, if z # y, then z O For any real numbers z and y. O For any real numbers r and y, if z # y, then z O For any real numbers z and y, if z # y, then I y is an integer, then y I is an integer y is an integer and y y is an integer or y y is not an integer and y I is an integer I is an integer I# y, then I I is not an integer y is not an integer or y – z is not an integer To show that Ris not anti-symmetric, we must find a counterexample satisfies which of the following statement? O For some real numbers z and y, z O For some real numbers z and y, I#y and r - y is an integer and y O For some real numbers r and y, r # y and z O For some real numbers z and y, r #y and z - y is not an integer and y- r is not an integer O For some real numbers z and y, r # y and z - y is not an integer or y y is an integer, and y -r is not an integer I is an integer I is an integer y is an integer or y z is not an integer

Let R be a relation on the set of all real numbers, where (x, y) E Rif and only if a y is an integer, To show that R is anti-symmetric, we must prove which of the following statement? O For any real numbers z and y, if z O For any real numbers z and y, if z # y, then z O For any real numbers z and y. O For any real numbers r and y, if z # y, then z O For any real numbers z and y, if z # y, then I y is an integer, then y I is an integer y is an integer and y y is an integer or y y is not an integer and y I is an integer I is an integer I# y, then I I is not an integer y is not an integer or y – z is not an integer To show that Ris not anti-symmetric, we must find a counterexample satisfies which of the following statement? O For some real numbers z and y, z O For some real numbers z and y, I#y and r - y is an integer and y O For some real numbers r and y, r # y and z O For some real numbers z and y, r #y and z - y is not an integer and y- r is not an integer O For some real numbers z and y, r # y and z - y is not an integer or y y is an integer, and y -r is not an integer I is an integer I is an integer y is an integer or y z is not an integer

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Let R be a relation on the set of all integers such that aRb if and only if a + b is even. To show that R is anti-symmetric, we must prove that For any integers a and b, if ab, then a + b is even and b + a is even For any integers a and b, if a + b, then a + b is even or b + a is even For any integers a and b, if ab, then a + b is odd or b+a is odd For any integers a and b, if ab, then a + b is odd and b + a is odd O For any integers a and b, if a + b is even, then b + a is even To show that R is not anti-symmetric, we must find a counterexample satisfies which of the following statement? For some integers a and b, a + b and a + b is odd and b + a is odd For some integers a and b, a + b and a + b is odd or b + a is odd For some integers a and b, a + b and a + b is even or b + a is even For some integers a and b, a b and a + b is even and b + a is even For some integers a and b, a + b is even and b + a is odd
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