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Let X = 1, 2,...

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Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let R1 be a relation in X given by R1 = {(x, y) : x – y is divisible by 3} and R2 be another relation on X given by R2 = {(x, y): {x, y} ⊂ {1, 4, 7}} or {x, y} ⊂ {2, 5, 8} or {x, y} ⊂ {3, 6, 9}}. Show that R1 = R2.

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Similar questions

R_{1}, R_{2}

are relation defined on

Z

a R_{1} b ⟺ (a - b)

is divisible by

3

a R_{2} b ⟺ (a - b)

is divisible by

4

. Then which of the two relation

(R_{1} \cup R_{2}), (R_{1} \cap R_{2})

is an equivalence relation?

R_{1}

be a relation from

A = {1, 3, 5, 7}

B = {2, 4, 6, 8}

R_{2}

be another relation from

B

C = {1, 2, 3, 4}

as defined below:

(i) An element

x

A

is related to an element

y

B

R_{1}

x + y

is divisible by 3.

(ii) An element

x

B

is related to an element

y

C

R_{2}

x + y

is even but not divisible by 3.

Which is the composite relation

R_{1} R_{2}

A

C

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 wether or not each of the relations

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

on A is
(a) reflexive
(b) symmetric
(c) transitive

A = {2, 3. 4, 5, 6, 7, 8, 9}

R

be the relation on

A

{(x, y) :

x \in A, y \in A

x

y}

. Find domain and range of

R

R_{1}

R_{2}

be equivalence relations on a set A, then

R_{1} \cup R_{2}

may or may not be:

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