Let A={1,2,3,4,5,6} and let R={(a,b):a,b∈A and b=a+1}. Show that R is not reflexive.

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Let A={1, 2, 3, 4, 5, 6} and let R={(a, b): a, b A and b=a+1}.

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Let $A = {1, 2, 3, 4, 5, 6}$ and let $R = {(a, b) : a, b \in A$ and $b = a + 1}$ . Show that R is not reflexive.

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Camila Discussed

Let

A = {1, 2, 3, 4, 5, 6}

and let

R = {(a, b) : a, b \in A

and

b = a + 1}

. Show that R is not reflexive.

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Given,

A = {1, 2, 3, 4, 5, 6}

R = {(a, b) : a, b \in A an d b = a + 1}

Reflexive Property

The Reflexive Property states that for every real number x,

x = x

when

a = 1, b = 1 + 1 = 2

so, we get,

(1, 2)

is possible, but

(1, 1)

is not possible, as

b = a + 1

and

1 \neq = 2 + 1

Symmetric Property

The Symmetric Property states that for all real numbers x and y,

x = y

, then

y = x

Transitive Property

The Transitive Property states that for all real numbers x ,y, and z,

x = y

and

y = z

, then

x = z

Therefore, R is not reflexive.

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Question Text	Let $A = {1, 2, 3, 4, 5, 6}$ and let $R = {(a, b) : a, b \in A$ and $b = a + 1}$ . Show that R is not reflexive.
Answer Type	Text solution:1
Upvotes	150

Let A={1,2,3,4,5,6} and let R={(a,b):a,b∈A and b=a+1}. Show that R is not reflexive.

Text solutionVerified

Practice questions from similar books

Let $A = {1, 2, 3, 4, 5, 6}$ and let $R = {(a, b) : a, b \in A$ and $b = a + 1}$ . Show that R is not reflexive.