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Relations and Functions
f : {1, 3, 4} → {1, 2, 5} is given by
f = {(1, 2), (3, 5), (4, 1)}
∴ f (1) = 2, f (3) = 5, f(4) = 1
Also g : {1, 2, 5} → {1, 3} is given by
g = {(1, 3), (2. 3), (5, 1)}
∴ g (1) = 3, g(2) = 3, g(5) = 1
Since co-domain of f is same as the domain of g
∴ g o f exists and (g o f) : {1,3,4 } → {1,3}
Now (g o f) (1) = g (f(1)) = g(2) = 3
(g o f)(3) = g (f(3)) = g(5) = 1
(g o f) (4) = g (f (4)) = g(1) = 3
∴ g o f = {(1, 3), (3, 1), (4, 3)}
Sponsor Area
Give an example of a relation which is
(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.
Sponsor Area
Sponsor Area