Question

Show that there is a bijection between set A = [−1, 3) to set B = (0, 1] ∪ [2, 3) by drawing a graph.

Answer 1

Answer with explanation:

⇒Set A = [-1,3)

There are infinite number of elements between two elements in a semi open sets.So,there are infinite number of elements between these two real numbers.

⇒Set B=(0,1]∪[2,3)

Similarly,there are infinite number of elements in the set B.

⇒The meaning of Bijection is that there should be one one correspondence between each members of two set.There should be no element in set B which do not have preimage in set A.Every element in A have unique Image in B.

⇒Both set A and Set B have infinite number of elements.That is these two sets are infinite sets.So,there is a bijection between two.