one-to-one correspondence

In the previous post we have discussed about truth table and In today's session we are going to discuss about one-to-one correspondence, It is a condition when all the elements of one set say set ‘T’ is matched with the member of other set say set ‘R’ . The other name of the one-to-one correspondence is bijection and bijective function. Here none of the member of the set remains unpaired. It means each element of one set is paired with the other element of the other set. The one-to-one correspondence from set T to set R has the inverted function from set T to set R. also we can say this if set T and set R has the finite number of elements then the presence of one-to-one correspondence states that the sets pursue the same number of element. One-to-one correspondence from all the sets to all members of the set are sometime termed as permutation. One-to-one correspondence also has many applications in many areas of mathematics which include definitions of permutation group, projective map, homeomorphism, etc.
To do the perfect pairing with between the set T and set R one-to-one correspondence must follow four properties, they are:

•  Each element of the set ‘T’ must be paired with one of the element of set ‘R’.
• Not even a single member of set ‘T’ should be repeated to form the pair with other member of set ‘R’.
• Each element of set ‘R’ must be matched with at least one element of set ‘T’.
  • None of the member of set ‘R’ can be paired with the more than one element of set ‘

If the one to one correspondence satisfies the first two properties than it is surjective in nature and if it satisfies the last two properties than it is injective in nature, Hence we can conclude this the one-to-one correspondence is both surjective and injective in nature.

You can also study the topic place value worksheets. And this topic you can find in the CBSE class 10 sample papers.