Home
Class 11
MATHS
Is it true that for any sets A and B, P...

Is it true that for any sets A and B, `P (A) uuP (B) = P (Auu B)`? Justify your answer.

Text Solution

AI Generated Solution

To determine whether the statement \( P(A) \cup P(B) = P(A \cup B) \) is true for any sets \( A \) and \( B \), we will analyze both sides of the equation step by step. ### Step 1: Define the Power Set The power set \( P(X) \) of a set \( X \) is the set of all subsets of \( X \). ### Step 2: Calculate \( P(A) \) and \( P(B) \) Let's consider two arbitrary sets: - Let \( A = \{a\} \) ...
Promotional Banner

Topper's Solved these Questions

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.6|8 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|32 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|7 Videos

Similar Questions

Explore conceptually related problems

For any two sets A and B, A' – B'=

Show that for any sets A and B ; A = (AnnB)uu(A-B) and Auu(B-A) = (AuuB)

For any sets A and B. show that P(A nnB) = P(A)nn P(B)dot

Given an example of a statement P(n) which is true for all ngeq4 but P(1),\ P(2)a n d\ P(3) are not true. Justify your answer.

Given an example of a statement P(n) which is true for all ngeq4 but P(1),\ P(2)a n d\ P(3) are not true. Justify your answer.

For any two sets A and B, prove that : P(A)=P(B)rArrA=B

Prove that Auu (Ann B)= A

Is it possible for rational numbers (a)/(b) and (b)/(a) , both in standard form, to be equal, given that a neb ? Justify your answer with examples.

Let f be the subset of Z xxZ defined by f = {(a b , a + b) : a , b in Z} . Is f a function from Z to Z? Justify your answer.

Let f be the subset of Z xxZ defined by f = {(a b , a + b) : a , b in Z} . Is f a function from Z to Z? Justify your answer.