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F:{(x,y):x is wife of y}

A={all human beings in a city}

check if reflexive transitive or symmetric

2
by sharmi

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A={all human beings in a city}

check if reflexive transitive or symmetric

by sharmi

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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.

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.