Question

((A ,B) A2+B2=1) on the sets has relation

Answer 1

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Let S be the set of all real numbers. Show that the relation R={(a,b):a

2

+b

2

=1} is symmetric but neither reflexive nor transitive.

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Solution

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(i) R is symmetric, since

aRb⇒a

2

+b

2

=1

⇒b

2

+a

2

=1⇒bRa.

(ii) R is not reflexive, since 1 is not related to 1, as

1

2

+1

2

=1 is not true.

(iii) Clearly,

2

1

R

2

3

and

2

3

R

2

1

But,

2

1

is not related to

2

1

as (

2

1

)

2

+(

2

1

)

2



=1.

∴R is not transitive

Answer 2

((A ,B) A2+B2=1) on the sets has a Symmetric relation.

What is Symmetric relation?

• A discrete mathematic relation between two or more elements of a set is such that if the first element is related to the second element, then the second element is also related to the first element
• The relation between any two elements of the set is symmetric
• A symmetric relation is a binary relation

We know that R = {(a, b): a2 + b2 = 1}

Consider (a, b) ∈ R where a2 + b2 = 1

We get (b, a) ∈ R and (a, b) ∈ R

Hence, R is symmetric.