Q. 225.0( 1 Vote )

If A = {1, 2, 3,

Answer :

Given A = {1, 2, 3, 4} and B = {a, b, c, d}.


We need to define bijections f1, f2, f3 and f4 from A to B.


Consider f1 = {(1, a), (2, b), (3, c), (4, d)}


(1) f1 is one-one because no two elements of the domain are mapped to the same element.


f1 is also onto because each element in the co-domain has a pre-image in the domain.


Thus, f1 is a bijection from A to B.


We have f1-1 = {(a, 1), (b, 2), (c, 3), (d, 4)}


Using similar explanation, we also have the following bijections defined from A to B -


(2) f2 = {(1, b), (2, c), (3, d), (4, a)}


We have f2-1 = {(b, 1), (c, 2), (d, 3), (a, 4)}


(3) f3 = {(1, c), (2, d), (3, a), (4, b)}


We have f3-1 = {(c, 1), (d, 2), (a, 3), (b, 4)}


(4) f4 = {(1, d), (2, a), (3, b), (4, c)}


We have f4-1 = {(d, 1), (a, 2), (b, 3), (c, 4)}


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