Question

Two points P and Q in a plane are related if OP=OQ, where O is a fixed point, This relation is
A.Partial order relation
B.Equivalence relation
C.Reflexive but not symmetric
D.Reflexive but not transitive

Answer 1

Should be B, but idk about A

Answer 2

But it's def not C or D

Answer 3

Answer is B
Can you explain ?

Answer 4

oww yea I got it right!

Answer 5

Equivalence relation means transitive, reflexive and symmetric. Equality is an equivalence relation since:
a=a (reflexive)
a=b;b=a (symmetric)
a=b=c means a=c (transitive)

Answer 6

ok i know that
but whats a, b and c here?

Answer 7

idk about A, but C says Reflexive but not symmetric, that means a=a, but if a=b, b doesn't have to equal a.

Answer 8

which is not true.

Answer 9

D.Reflexive but not transitive
that means
a=a
but if a=b=c, a does not have to equal a, which is not true either

Answer 10

no no i'm asking about
a,b,c you mentioned here

"a=a (reflexive)
a=b;b=a (symmetric)
a=b=c means a=c (transitive)"

Answer 11

what is a,b,c in this question (not the options)

Answer 12

OP=OQ
Equality is an equivalence relation, i was just using a and b and c as examples.

Answer 13

to show properties of equality

Answer 14

ok why not other options?

Answer 15

I just explained why it's not C or D. Idk what A is, but I was guessing B lol

Answer 16

Because partial order didn't seem right.

Answer 17

Definition(equivalence relation): A binary relation R on a set A is an equivalence relation if and only if
(1) R is reflexive
(2) R is symmetric, and
(3) R is transitive.

Binary Relation: Equality
Set A: {OP, OQ}
1) Reflexive: OP = OP and OQ = OQ
2) Symmetric: If OP = OQ, then OQ = OP
3) Transitive: If OP = OQ and OQ = OP, then OP = OP

Answer 18

On a Multiple Choice Question, the task, unless otherwise stated, is the select the BEST answer from those provide. Equivalence Relation subsumes the other options you might choose. That it, option B includes those others. So, B is the best answer.

While many people view multiple choice questions as "easy," such questions are not always so due to the lack of mathematics background or the lack of precise verbal skills of the person who wrote the question.

Answer 19

Thank you so much! :)