let R BE THE RELATION FROM N TO N defined by R={(a,b)}: a,b belong to natural nos and a=b^2 are the following true
1) (a,a) belongs to R , FOR ALL a belong to N
2) (a,a) belong to R implies (b,a) belong to R
3) (a,a) belong to R, (b,c) belong to R implies (a,c) belong to R
the ans to all is no so plzzzzzzzzzz explain
Moderation Team
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![[tex] \\ \mbox{For the benefit of everyone ...always see to that that u type the question ..}\\ \\ \mbox{The question goes like this} \\ \mbox{Let R be a relation from N to N defined by R=[(a,b):a,b belongs to N and } \ a=b^2] \\ \\ \mbox{State if the following are true or false} \\ \mbox{1.(a,a) belongs to N for all a belonging to N} \\ \mbox{Answer: See ..to prove something is false ..an example is enough..so as (2,2) does not belong to R} \\ \mbox{first statement is false} \\ \\ \mbox{2.(a,b) belongs to R means (b,a) belongs to R} \\ \mbox{This is also false because (4,2) belongs to R but (2,4) does not belong} \\ \\ \mbox{3.(a,b) belongs to R,(b,c) belongs to R implies (a,c) belongs to R} \\ \mbox{False ..because (16,4) belongs to R and (4,2) belongs to R but (16,2) does not belong to R}\\ \\ \mbox{Thus all assertions are wrong}[\tex]](http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/d/2/9/d2910d345d2cb148089b9103d3d8338f9da4d9d0.gif)
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