relations

Question

what is the Number of relations S over set {0,1,2,3} such that (x,y) belongs to S=> x=y

Comments

2^4=16

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16??

Answer 1

There are four elements in your set. Relation says x=y thus an element can be related to itself only. Now for any element of the set S we have two choices: include it or discard it in the relation set . So 2⁴ 

Comments

@manu00x I think your solution is correct as if we do cross product between same set we will get 16 pairs of (x,y) and in that 4 are mandatory to be in the resultant relation i.e. (0,0) (1,1) (2,2) (3,3)

and remaing are 12 so for those 12 we have 2 choices i.e. {include in relation or not}

so 2^12 = 4096 is correct.

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I think 4096 is the correct answer as they are indirectly saying calculate total no of reflexive relation on S.

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=> implies Mathematical logic

It is given that (x,y) belongs to S => x=y. Now consider a pair (1,2), if it belongs to relation then 1=2 is false (True => False). Actually we have to consider a pair and see (True => True). IT is not asking for reflexive relations.