Question 1182111: The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana.
Alabama Arkansas Louisiana
soybeans (s) soybeans (s) soybeans (s)
peanuts (p) rice (r) sugarcane No
corn (c) cotton (t) rice (r)
hay heart hay heart corn (c)
wheat (w) wheat (w) cotton (t)
Let U be the smallest possible universal set that includes all of the crops listed; and let A, K, and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.
K ∪ L
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Table:
| Alabama | Arkansas | Louisiana | | soybeans (s) | soybeans (s) | soybeans (s) | | peanuts (p) | rice (r) | sugarcane No | | corn (c) | cotton (t) | rice (r) | | hay heart | hay heart | corn (c) | | wheat (w) | wheat (w) | cotton (t) |
To be honest, I'm not sure what your teacher meant by "sugarcane no", but I have a feeling it was supposed to be some kind of symbol.
Regardless, I'll just list the crops in word format.
K = set of crops from Arkansas
K = {soybeans, rice, cotton, hay, wheat}
We simply just list everything in the second column of the table above.
L = set of crops from Louisana
L = {soybeans, sugarcane, rice, corn, cotton}
Same idea but we look at the third column now.
The set K u L is the following
K u L = {soybeans, rice, cotton, hay, wheat, sugarcane, corn}
What I did was start with set K. Then I added items from set L such that I didn't repeat any crops. With any set, we simply list the item once and only once. No repeats are allowed. The order of the set doesn't matter.
The 'u' refers to "set union". Think of two people getting married and forming a union together. When they move in together, the bride and groom's various stuff (eg: couch, fridge, etc) will go from 2 separate houses to one house. The house represents the set while the furniture are the elements of the set. When forming a set union, we don't have repeated elements, so for example they won't have two fridges when they move in together.
Here's another example of a set union
A = {p,q,r}
B = {p,s,w}
A u B = {p,q,r, s,w}
We don't list the item 'p' a second time.
Note: be sure not to mix up the union symbol with the universal set notation. Unfortunately both look nearly identical.
Answer: {soybeans, rice, cotton, hay, wheat, sugarcane, corn}
Replace the words with their corresponding symbols if your teacher requires it.
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