| Q. | Let ๐ = {1,2, โฆ , ๐}. Let ๐ด = {(๐ฅ, ๐)|๐ฅ โ ๐, ๐ โ ๐}. Consider the following two statements on |๐ด|. I. |๐ด| = ๐2๐โ1 II. |๐ด| = โ๐๐=1 ๐(๐) Which of the above statements is/are TRUE? | |
| (A) Only I | (B) Only II | |
| (C) Both I and II | (D) Neither I nor II | |
Given, A = {(x, X)โฃ xโX, XโU }, where U = {1, 2, โฆ,n}.
As we know that The number of k element subsets of a set U with n elements =nCk.
The number of possible ordered pairs (x, X) where x โ X is kโ nCkfor a given value of k from 1 to n. So total number of ordered pairs in A,
