Question

Let R be a binary relation defined as R = {(a, b) € R^2 : (a - b) ≤ 3) Determine whether R is reflexive, symmetric, antisymmetric and transitive.

Chapter: Relations.
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Answer 1

Answer:

are the guestions using verbs in the simple future the future continuous 1. What will you be doing tomorrow at 6 p.m.? 2. When will the doctor arrive? 3. Where will you go for your vacation? 4. Who will prepare the charts? 5. What will you be doing at 7.30 p.m. on Monday? .

lost moon while counting stars..jiski parwah nhi thi vo intzar krta krta chla gya jiski thi vo bin kdr kiy chla gya

Answer 2

Answer:

The given relation is reflexive and symmetric but not antisymmetric and transitive.

Step-by-step explanation:

Given R is a binary relation defined as

$R = \{(a, b) \in R^2 : (a - b) \le 3\}$

Here R is set of square of the real numbers and both a and b are real numbers.

1. If the relation is reflexive, then $(a,a)\in R$

  Let a be any arbitrary element of $R^{2}$, $a\in R^2$

  then, $| a - a|=0 \le 3$

  So, the given relation is reflexive.

2. The relation is symmetric, when $(a,b)\in R$ then $(b,a)\in R$

   Since $| a - b|=|b - a|$

   If  $| a - b|\le 3$ then, $| b - a| \le 3$

   So, the given relation is symmetric.

   Since the relation is symmetric it can not be antisymmetric.

3. The relation is transitive,

    if $(a,b)\in R$ and $(b,c)\in R$ then $(a,c)\in R$

    Let  $(1,4)\in R^2$ and $(4,9)\in R^2$

    then $| 1 - 4|\le 3$ and $| 4- 9| > 3$

    So, the transitive property doesn't exists to the given relation.

Hence, the given relation is reflexive and symmetric but not antisymmetric and transitive.

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