Answer:
1.U={1,2,3,4,5}
A={2}
B={2,3}
C={4,5}
2.U={1,2,3,4}
A={1,2}
B={2,3}
C={4}
Step-by-step explanation:
We are given that
and ![A\cup (B\cap C)](https://tex.z-dn.net/?f=A%5Ccup%20%28B%5Ccap%20C%29)
are different sets
1.We have to construct a universe set U and non empty sets A,B and C so that above set in fact the same
Suppose U={1,2,3,4,5}
A={2}
B={2,3}
C={4,5}
![B\cap C=\phi](https://tex.z-dn.net/?f=B%5Ccap%20C%3D%5Cphi)
{2,3,4,5}
={2}
{2,3,4,5}={2}
={2}
={2}
Hence, ![A\cap (B\cup C)=A\cup (B\cap C)](https://tex.z-dn.net/?f=A%5Ccap%20%28B%5Ccup%20C%29%3DA%5Ccup%20%28B%5Ccap%20C%29)
2.We have to construct a universe set U and non empty sets A,B and C so that above sets are in fact different
Suppose U={1,2,3,4}
A={1,2}
B={2,3}
C={4}
![B\cap C=\phi](https://tex.z-dn.net/?f=%20B%5Ccap%20C%3D%5Cphi)
={2,3,4}
={1,2}
={1,2}
={1,2}
{2,3,4}={2}
Hence, ![A\cap (B\cup C)\neq A\cup (B\cap C)](https://tex.z-dn.net/?f=A%5Ccap%20%28B%5Ccup%20C%29%5Cneq%20A%5Ccup%20%28B%5Ccap%20C%29)
that's right the way you have it right now in the picture all adds up to 65
Answer:
192
Step-by-step explanation:
Well if the first rectangle is 72 and 56, then we can find the area of that by multiplying length times width which would be 4032, so that would be the area of the second one. then we divide 4032 by 21, which is 192.
P.S, This is my first question answered, so if im wrong please let me know, thank you!
Answer:
The volume is 191.3 ![cm^3](https://tex.z-dn.net/?f=cm%5E3)
Step-by-step explanation:
Recall that the formula for the volume of a pyramid is given by the formula:
![Volume=\frac{B\,*H}{3}](https://tex.z-dn.net/?f=Volume%3D%5Cfrac%7BB%5C%2C%2AH%7D%7B3%7D)
where B is the area of the pyramid's base, and H its height. So, in our case, the base is a square of length 7.5 cm, which gives 56.25 cm^2
Now, we use this value and the height 10.2 cm to find the volume:
![Volume=\frac{B\,*H}{3}\\Volume=\frac{56.25\,*10.2}{3}\\Volume=191.25\,\,cm^3](https://tex.z-dn.net/?f=Volume%3D%5Cfrac%7BB%5C%2C%2AH%7D%7B3%7D%5C%5CVolume%3D%5Cfrac%7B56.25%5C%2C%2A10.2%7D%7B3%7D%5C%5CVolume%3D191.25%5C%2C%5C%2Ccm%5E3)
which rounded to the nearest tenth is: 191.3 ![cm^3](https://tex.z-dn.net/?f=cm%5E3)