Answer with Step-by-step explanation:
We are given that A, B and C are subsets of universal set U.
We have to prove that
![A\cap (B-C)=(A\cap B)-(A\cap C)](https://tex.z-dn.net/?f=%20A%5Ccap%20%28B-C%29%3D%28A%5Ccap%20B%29-%28A%5Ccap%20C%29)
Proof:
Let x![\in A\cap (B-C)](https://tex.z-dn.net/?f=%5Cin%20A%5Ccap%20%28B-C%29)
Then
and ![x\in(B-C)](https://tex.z-dn.net/?f=x%5Cin%28B-C%29)
When
then
but ![x\notin C](https://tex.z-dn.net/?f=x%5Cnotin%20C)
Therefore,
but ![x\notin (A\cap C)](https://tex.z-dn.net/?f=%20x%5Cnotin%20%28A%5Ccap%20C%29)
Hence, it is true.
Conversely , Let
but ![x\notin(A\cap C)](https://tex.z-dn.net/?f=x%5Cnotin%28A%5Ccap%20C%29)
Then
and
When
then ![x\notin C](https://tex.z-dn.net/?f=x%5Cnotin%20C)
Therefor,![x\in A\cap (B-C)](https://tex.z-dn.net/?f=x%5Cin%20A%5Ccap%20%28B-C%29)
Hence, the statement is true.
Answer:
Obtuse
Step-by-step explanation:
One of the angles is above 90 degrees
700% increase.
Step-by-step explanation:
The duration was 3 decades, or 30 years. The population starts at 100%, then doubles to 200% (decade 1), then 400% (decade 2), then 800% (decade 3).
800% - 100% = 700%
Should be all real numbers