Step-by-step explanation:
(a)
Using the definition given from the problem 
![f(A) = \{x^2  \, : \, x \in [0,2]\} = [0,4]\\f(B) = \{x^2  \, : \, x \in [1,4]\} = [1,16]\\f(A) \cap f(B) = [1,4]  = f(A \cap B)\\](https://tex.z-dn.net/?f=f%28A%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B0%2C2%5D%5C%7D%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B1%2C4%5D%5C%7D%20%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccap%20f%28B%29%20%3D%20%5B1%2C4%5D%20%20%3D%20f%28A%20%5Ccap%20B%29%5C%5C)
Therefore it is true for intersection. Now for union, we have that 
![A \cup B = [0,4]\\f(A\cup B ) = [0,16]\\f(A) = [0,4]\\f(B)= [1,16]\\f(A) \cup f(B) = [0,16]](https://tex.z-dn.net/?f=A%20%5Ccup%20B%20%3D%20%5B0%2C4%5D%5C%5Cf%28A%5Ccup%20B%20%29%20%3D%20%5B0%2C16%5D%5C%5Cf%28A%29%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccup%20f%28B%29%20%3D%20%5B0%2C16%5D)
Therefore, for this case, it would be true that  .
. 
(b)
1 is not a set. 
(c)
To begin with   

Therefore 

Now, given an element of  it will belong to both sets, therefore it also belongs to
 it will belong to both sets, therefore it also belongs to  , and you would have that
, and you would have that 
 , therefore
, therefore   .
. 
(d)
To begin with  , therefore
, therefore 

 
        
             
        
        
        
Answer:
Step-by-step explanation:
The volume is calculated like:
V= length* hauteur* wide
V= 5* 2 3/4* 10 1/2

 
        
             
        
        
        
No because if you convert them into a percentage, you get 11/15 as 73.3% and 1/2 is 50%. Hope this helps