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1. If she is my friend and you are her friend, then we are friends. Given this, the friend relationship in this context is ________________.
(i) Commutative (ii) transitive (iii) implicative (iv) equivalence
(A) (i) and (ii) (B) (iii) (C) (i),(ii),(iii) and (iv) (D) None of these

2 Answers

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Let Consider, 

I am assigning A to myself, B to my beautiful friend wink, and You are C. 

Then $(P,Q)$ means P is friend of Q

Then,

She is my friend means I am friend of her i.e. (A,B).

You are her friend means (C,B). 

We are friend means I am your friend i.e. (A, C) 

Now Relation R = { (A,B), (C,B), (A,C) }

This relation has (A,B) but does not have (B,A) hence its can not be commutative. 

Since its is not commutative, hence it can not be equivalence. 

Its Transitive, because set has (A.C), (C, B) and also has (A,B).

And its not Implicative also.

But there in no option only for transitivity. Hence answer will be D) None of the above

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Answer C)

you are her friend-(A,B)

she is my friend-(B,C)

(A,B) and (B,C) hold then friends relation holds for all

So, here transitivity holds

And we are friends holds other properties too

So, all property will satisfy here

edited by

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