Q. 74.2( 89 Votes )

Let A = {1, 2}, B

Answer :

(i) Given: A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}

To verify: A × (B C) = (A × B) (A × C)


As we see,


By definition if either of the two set P and Q is null set then P × Q will also be a null set. i.e. P × Q = ϕ .



Now, (A × B) = {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4)}


And (A × C) = {(1,5), (1,6), (2,5), (2,6)}



From (1) and (2)



(ii) Given: A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}


To verify: A × C is a subset of B × D.


(A × C) = {(1,5), (1,6), (2,5), (2,6)}


(B × D) = {(1,5), (1,6), (1,7), (1,8), (2,5), (2,6), (2,7), (2,8), (3,5), (3,6), (3,7), (3,8), (4,5), (4,6), (4,7), (4,8)}


As we see all the elements of set A × B are there in set B × D.


Hence, A × C is a subset of B × D.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Let A = {1,2,3,4}NCERT - Maths

If A = {–1, 1}, fNCERT - Maths

If the set A has NCERT - Maths

Let A and B be twNCERT - Maths

Let A = {1, 2} anNCERT - Maths

If A × B = {(a, xNCERT - Maths