Question

If n(A)=P, n(B)=q then the total number of relations that exist between A and B is
(a) 2
(b) 2q
(c) 2P+q
(d) 2pq​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{A and B are two sets such that}$

$\mathsf{n(A)=p\;and\;n(B)=q}$

$\underline{\textbf{To find:}}$

$\textsf{Total number of relations between A and B}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\boxed{\textbf{Number of subsets of set having 'm' elements is 2^m }}$

$\textsf{Total number of relations between A and B}$

$\textsf{=Total number of subsets of}\;\mathsf{A{\times}B}$

$\mathsf{=2^{n(A{\times}B)}}$

$\mathsf{=2^{n(A)\,{\times}\,n(B)}}$

$\mathsf{=2^{p{\times}q}}$

$\mathsf{=2^{pq}}$

$\underline{\textbf{Answer:}}$

$\textsf{Option\;(d)\;is\;correct}$

$\underline{\textbf{Find more:}}$

If U={x:x in N x<=30} A={x:x is prime <5} B={x:x is a perfect square <=10} and C={x:x is a perfect cube <=30} then verify the following results : (i) (A uu B)'=A'nn B' (ii)(A nn B)'=A'uu B' (iii) (A nn B)nn C=A nn(B nn C) (iv) A'-B'=B-A

https://brainly.in/question/19022578

Answer 2

Answer:

Step-by-step explanation: