Database-Management-System
April 2, 2025UGC NET CS 2006 Dec-paper-2
April 2, 2025GATE 2021 CS-Set-2
| Question 63 |
| There exists a bijection from S1to S2. | |
| There does not exist a bijection from S1to S2. | |
| There exists a surjection from S1to S2. | |
| There does not exist an injunction from S1to S2. |
Question 63 Explanation:
The number of functions from a set A to set B is |B|^|A|.
S2: |B|= 3, |A|= n^2-1 +1 = n^2.
we have number of functions 3^(n^2).
S1: there are n*n positions in a matrix of size nxn. Each can be filled with either 0 or 1 or 2 i,e, in 3^(n^2)
As there are equal number of elements on both sides, S1->S2 can be one one , onto as well bijection
Correct Answer: C
Question 63 Explanation:
The number of functions from a set A to set B is |B|^|A|.
S2: |B|= 3, |A|= n^2-1 +1 = n^2.
we have number of functions 3^(n^2).
S1: there are n*n positions in a matrix of size nxn. Each can be filled with either 0 or 1 or 2 i,e, in 3^(n^2)
As there are equal number of elements on both sides, S1->S2 can be one one , onto as well bijection