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Please Solve R.D. Sharma class 12 Chapter relations Exercise 1.1 Question 13 Maths textbook Solution.

Answers (1)

Answer:

Hence proved, the relation “ $\geq$ ” on the set $R$ of all real numbers is reflexive and transitive but not symmetric.

Hint:

A relation $R$ on set $A$ is

Reflexive relation:

If $(a, a) \in R$ for every $a \in A$

Symmetric relation:

If $(a, b)$ is true then $(b, a)$ is also true for every $a, b \in A$

Transitive relation:

If $(a, b) \text { and }(b, c) \in R$ then $(a, c) \in R$ for every $a, b, c \in A$

Given:

Relation is ” $\geq$ ”on the $R$ of all real numbers.

Solution:

Reflexivity:

Let $a \in R$

$a \geq a$

" $\geq$ "is reflexive.

Transitive:

Let $a, b, c \in R$

Such that $a \geq b \text { and } b \geq c$

Then $a \geq c$

$" \geq "$ is transitive.

Symmetric: Let $a, b \in R$

Such that $a \geq b \text { but } b \ngeqslant a$

$" \geq "$ not symmetric

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