ZoologyState true or false.Let S be a relation on the set R of all real numbers defined byS=(a,b)∈R×R:a2+b2=1 then S is not an equivalence relation on R.

State true or false.

Let S be a relation on the set R of all real numbers defined by

$S = \{(a, b) \in R \times R : a^{2} + b^{2} = 1\}$ then S is not an equivalence relation on R.

A
True
B
False

Solution:

Given relation is,

S = \{(a, b) \in R \times R : a^{2} + b^{2} = 1\}

Here,

(1, 1) \in R \times R

but,

(1, 1) \notin S

As,

1^{2} + 1^{2} = 2 \neq 1

.
So, we can say that given relation is not reflexive.
Now, a relation which is reflexive, transitive as well as symmetric is known as equivalence relation.
Here, relation cannot be equivalence relation as it is not reflexive.
So, given statement is true.
Correct option is 1.

State true or false.

Let S be a relation on the set R of all real numbers defined by

$S = \{(a, b) \in R \times R : a^{2} + b^{2} = 1\}$ then S is not an equivalence relation on R.

Solution:

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