f:{(x,y):x is wife of y}
A={all human beings in a city}
check if reflexive transitive or symmetric
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Answered by
2
it is not reflexive as x cant be a wife of x
it is not symmetric because if x is wife of y then y is not wife of x
it is transitive as - x is the wife of y , so y is male n cant be a wife to any random z. there is no point in checking further if x can be wife of z or not. hence it is transitive but not reflexive or symmetric.
it is not symmetric because if x is wife of y then y is not wife of x
it is transitive as - x is the wife of y , so y is male n cant be a wife to any random z. there is no point in checking further if x can be wife of z or not. hence it is transitive but not reflexive or symmetric.
Answered by
1
For reflexive
(a,a)∈F
It is not reflexive because (a,a)∉F because a cannot be wife of a
For symmetric
(a,b)∈f then (b,a) should ∈f
It is not transitive because if (a,b)∈f means a is wife of b ,but for transitive (b,a) should belongs to f which is not possible b cannot be wife of a
For transitive
(a,b)∈f,(b,c)∈f
It is not symmetric because if (a,b)∈f means a is wife of b then (b,c)∉f because a is female which cannot comes as male.according to situation.
(a,a)∈F
It is not reflexive because (a,a)∉F because a cannot be wife of a
For symmetric
(a,b)∈f then (b,a) should ∈f
It is not transitive because if (a,b)∈f means a is wife of b ,but for transitive (b,a) should belongs to f which is not possible b cannot be wife of a
For transitive
(a,b)∈f,(b,c)∈f
It is not symmetric because if (a,b)∈f means a is wife of b then (b,c)∉f because a is female which cannot comes as male.according to situation.
namku:
this is wrong. the function is transitive. i think ur concept of transitivity is not clear
u are right,there is replacement of transitive and symmetry
I have done mistake
yup . my answer above is right. it is only transitive. it is not reflexive or symmetric.
How can it possible.(a,b) belongs to F means a is wife of b and (b,c) belongs to f means b is wife of c.From (a,b) we sees that a is female and b is male and from (b,c) we sees that b is female and c is male.Contradiction.cannot possible.It is not transitive
dude if a.b belongs to F and b.c belongs to F and a.c doesnt belong to F then we can say it is not transitive. here b.c only doesnt belong to F so it is not contradicting transitivity. check ncert or any other book and get ur concepts right . it is not a direct question it is a tricky question. u can check from any other resource.
okk
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