Let A -1- 2- 3 and let R1-1-1- 1- 3- 3- 1 2- 2 2- 1- 3- 3 R2 - 2- 2- 3- 1- 1- 3 R3 - 1- 3- 3- 3 R4 - A- AFind wether or not each of the relations R1- R2- R3- R4- on A is a reflexiveb symmetricc transitive

#160;(i) R but not #160; S as (2, 1) ∈ R_1 but (1, 2) ∉ R_1 not T as (2, 1) and (1, 3) ∈ R_1 but (2, 3) ∉ R_1 (ii) ≠ R as all li ...

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Byju's Answer

Standard XII

Mathematics

Symmetric Relations

Let A =1, 2, ...

Question

Let A ={1, 2, 3} and let
$R_{1}$ ={(1,1),( 1, 3), (3, 1) (2, 2) (2, 1), (3, 3)}
$R_{2}$ = {(2, 2), (3, 1), (1, 3) }
$R_{3}$ = {(1, 3), (3, 3)}
$R_{4} = A \times A$
Find wether or not each of the relations $R_{1}, R_{2}, R_{3}, R_{4},$ on A is
(a) reflexive
(b) symmetric
(c) transitive

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Solution

(i) R but not S as (2, 1) $\in R_{1}$ but (1, 2) $\notin R_{1}$ not T as (2, 1) and (1, 3) $\in R_{1}$ but (2, 3) $\notin R_{1}$
(ii) $\neq R$ as all like pairs are not there. It is S but not T as (3, 1) and (1, 3) $\in R_{2}$ but (3, 3) $\notin R_{2}$
(iii) $\neq R, \neq S$ but it is T.
(iv) R, S, T all as $A \times A$ contains all possible ordered pairs.

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Similar questions

Q. In the circuit shown if

R_{1} : R_{2} : R_{3} : R_{4} = 1 : 2 : 3 : 4

then_____

Q. Three rivers

R_{1}, R_{2}

and

R_{3}

merge together to form a river,

R_{4}

. The cross sectional areas of the three rivers

R_{1}, R_{2}

and

R_{3}

are in the ratio

1 : 2 : 3

and speed of water flowing in these are in the ratio

1 : \frac{1}{2} : \frac{1}{3}

. Assuming streamline flow, if

R_{4}

has cross sectional area equal to that of

R_{1}

, the ratio of speed of water in

R_{4}

to that in

R_{1}

Q. Let

A = {1, 2, 3}

and let

R_{1} = {(1, 1), (1, 3) (3, 1) (2, 2), (2, 1) (3, 3)}

R_{2} = {(2, 2), (3, 1), (1, 3)}

R_{3} = {(1, 3), (3, 3)}

R_{4} = A \times A .

Find which of the given each of the relations

R_{1}, R_{2}, R_{3}, R_{4},

on A satisfy all the given properties:

(a) reflexive (b) symmetric (c) transitive

Let A = {p. q, r, s} and B = {1, 2, 3}. Which of the following relations from A to B is not a function?
(i) $R_{1} = {(p, 1), (q, 2), (r, 1), (s, 2)}$
(ii) $R_{2} = {(p, 1), (q, 1), (r, 1), (s, 1)}$
(iii) $R_{3} = {(p, 1), (q, 2), (r, 1), (s, 2)}$
(iv) $R_{4} = {(p, 2), (q, 3), (r, 2), (s, 2)}$

Q. Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?

(a) R₁ = [(p, 1), (q, 2), (r, 1), (s, 2)]
(b) R₂ = [(p, 1), (q, 1), (r, 1), (s, 1)]
(c) R₃ = [(p, 1), (q, 2), (p, 2), (s, 3)
(d) R₄ = [(p, 2), (q, 3), (r, 2), (s, 2)].

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Let A ={1, 2, 3} and let R1={(1,1),( 1, 3), (3, 1) (2, 2) (2, 1), (3, 3)}R2 = {(2, 2), (3, 1), (1, 3) }R3 = {(1, 3), (3, 3)}R4=A×AFind wether or not each of the relations R1,R2,R3,R4, on A is (a) reflexive(b) symmetric(c) transitive

(i) R but not S as (2, 1)∈R1 but (1, 2)∉R1 not T as (2, 1) and (1, 3) ∈R1 but (2, 3) ∉R1(ii) ≠R as all like pairs are not there. It is S but not T as (3, 1) and (1, 3) ∈R2 but (3, 3) ∉R2(iii) ≠R,≠S but it is T.(iv) R, S, T all as A×A contains all possible ordered pairs.

Let A ={1, 2, 3} and let
$R_{1}$ ={(1,1),( 1, 3), (3, 1) (2, 2) (2, 1), (3, 3)}
$R_{2}$ = {(2, 2), (3, 1), (1, 3) }
$R_{3}$ = {(1, 3), (3, 3)}
$R_{4} = A \times A$
Find wether or not each of the relations $R_{1}, R_{2}, R_{3}, R_{4},$ on A is
(a) reflexive
(b) symmetric
(c) transitive