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

Prove that : A(BC)=(AB)(AC) without using venn diagram.

Open in App
Solution

If A(BC)=ϕ then the result holds by properties of ϕ. So assume
A(BC)ϕ and let xA(BC)
The xA and xBC which implies that xA and (xB,xC)
Case 1:
xB
if xC, then xAC which is x(AB)(AC)
Case 2
xB
If xC, then xAC which means
x(AB)(AC)
Both cases lead to the same conclusion
x(AB)(AC)
Hence
A(BC)(AB)(AC)
Hence proved


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Set Operation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon