Question-157887

Question Number 157887 by Tawa11 last updated on 29/Oct/21

Commented by Tawa11 last updated on 29/Oct/21

Proof please

Commented by Rasheed.Sindhi last updated on 29/Oct/21

f i s n o t a f u n c t i o n . {I t}^{'} s a r e l a t i o n .

B e c a u s e f (3) i s n o t u n i q u e .

Answered by Rasheed.Sindhi last updated on 29/Oct/21

f = {(β, a), (3, b), (3, c)}

f (β) = a, f (3) = b, f (3) = c

g = {(a, 3), (b, β), (c, β)}

g (f (β)) = g (a) = 3

g (f (3)) = g (b) = β

g (f (3)) = g (c) = β

g o f = {(β, 3), (3, β)}

g = {(a, 3), (b, β), (c, β)}

g (a) = 3, g (b) = β, g (c) = β

f = {(β, a), (3, b), (3, c)}

f (g (a)) = f (3) = b, c

f (g (b)) = f (β) = a

f (g (c)) = f (β) = a

f o g = {(a, b) (a, c) (b, a), (c, a)}

Commented by Tawa11 last updated on 29/Oct/21

God bless you sir

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