wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let A = {10, 15, 20, 25, 30, 35, 40, 45 } 50 , B = { 1, 5,10,15, 20, 30} and C = { 1, 5,15, 20, 35, 45, }. Verify A(BC)=(AB)(AC).

Open in App
Solution

The given sets are A={10,15,20,25,30,35,40,45,50}, B={1,5,10,15,20,30} and C={1,5,15,20,35,45}

Let us first find A(BC) as follows:

A(BC)={10,15,20,25,30,35,40,45,50}({1,5,10,15,20,30}{1,5,15,20,35,45})
={10,15,20,25,30,35,40,45,50}{1,5,15,20}={10,25,30,35,40,45,50}........(1)

Now we find (AB)(AC)as follows:

(AB)(AC)
=({10,15,20,25,30,35,40,45,50}{1,5,10,15,20,30})({10,15,20,25,30,35,40,45,50}
{1,5,15,20,35,45})
={25,35,40,45,50}{10,25,30,40,50}={10,25,30,35,40,45,50}........(2)

Since equation 1 is equal to equation 2,

Hence, A(BC)=(AB)(AC)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Operations on Sets
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon