Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
4.5k views
in Sets, Relations and Functions by (26.1k points)
closed by

If U = {1,2,3,4,5,6,7,8,9,10,12,24} 

A = {x ∶ x is prime number and x ≤ 10} 

B = {x ∶ x is a factor of 24} 

Verify the following result 

(i) A – B = A ∩ B’ 

(ii) (A ∪ B)’ = A’ ∩ B’ 

(iii) (A ∩ B)’ = A’ ∩ B’

1 Answer

+1 vote
by (26.7k points)
selected by
 
Best answer

Given, U = {1,2,3,4,5,6,7,8,9,10,12,24} 

A = {2,3,5,7}  

B = {1,2,3,4,5,6,8,12,24}  

Now, A’ = {1,4,6,8,9,10,12,24} 

B’ = {5,7,9,10} 

A ∪ B = {1,2,3,4,5,6,7,8,12,24} 

(A ∪ B)’ = {9,10} 

A ∩ B = {2,3} 

(A ∪ B)’ = {1,4,5,6,7,8,9,10,12,24} 

(i) A – B = A ∩ B’ 

L.H.S = A – B = {2,3,5,7} – {1,2,3,4,6,8,12,24} = {5,7} 

R.H.S = A ∩ B’ = {2,3,5,7} ∩ {5,7,9,10} = {5,7} 

∴ L.H.S = R.H.S,  

(ii) (A ∪ B)’ = A ∩ B’ 

L.H.S = (A ∪ B)’ = {9,10} 

R.H.S = A’∩ B’ = {1,4,6,8,9,10,12,24} ∩ {5,7,9,10} = {9,10} 

∴ L.H.S = R.H.S,  

(iii) (A ∩ B)’ = A’ ∩ B’ 

L.H.S = (A ∩ B)’ = {1,4,5,6,7,8,9,10,12,24} 

R.H.S = A’ ∩ B’ = {1,4,6,8,9,10,12,24} ∩ {5,7,9,10} = {1,4,5,6,7,8,9,10,12,34} 

∴ L.H.S = R.H.S,

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...