Notes:
The notation ">=" without quotes means "greater than or equal to"
The upper case "U" means "set union"
Instead of using the intersection symbol, I will use a lower case 'n'
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Problem 1
A = {x | x < 1} which is the set of x values smaller than 1
B = {x | x >= 5} is the set of x values that are equal to 5 or larger
A U B = set of values that are from set A OR they are from set B (or both)
A U B = {x | x < 1 or x >= 5}
we simply connect the two inequalities mentioned with an "or"
note: how there is no overlap between the two regions. The "U" means "set union" which is like a sort of glue to tie the two sets together with an "or".
Answer: {x| x < 1 or x >= 5}
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Problem 2
A = {x | x < 1}
C = {x | x = 5} which is the set of one value only: 5 (x cannot equal any other value)
A U C = {x| x < 1 or x = 5}
So if a number is in set A U C, then this number is either less than 1, OR it is equal to 5
Answer: {x|x < 1 or x = 5}
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Problem 3
B U C = {x | x >= 5} because set C already has the "or equal to" part in there.
Set C is a subset of set B. If an item is in set C, then it is also in set B.
Answer: {x| x >= 5}
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Problem 4
Again recall that I'm using an 'n' to indicate "set intersection" instead of the upside down "U" symbol
A n B is the set of items that are in BOTH sets A and B at the same time. From problem 1, I mentioned there's a gap. There is no x value that is both less than 1 AND greater than or equal to 5. So this means that
A n B = empty set
which we use the "O" with a slash through it. This is a special symbol to indicate "empty set"
Another way to write "empty set" is to use curly braces with nothing inside like so { }
Answer: The "O" with a slash through it
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Problem 5
B n C is the same as {x| x = 5}
Why? Because if an item is in B n C, then it has to be in BOTH set B and set C at the same time. The only way this happens is if x = 5. If x is any other value, then it won't be in set C
Answer: {x| x = 5}
Answer:
An advertisement.
Step-by-step explanation:
It's called a Celebrity Endorsement but it's a subgroup of an Advert.
Answer:
1. 21.6
2. 54
3.16.22
Step-by-step explanation:
1. 3(1.8)(4)
2. 7.5(1.8)(4)
3. (1.4)(4) + (5.9)(1.8)
The formula for circumference is πd.
Diameter is 2r.
5 x 2 = 10
Use 3.14 for π.
10 x 3.14 = 31.4 yards
Answer:
Step-by-step explanation:
our expression is
we are asked to simplify the expression
in order to that we first bring the like terms together
like terms are those having the same variable or same combination of variables with exactly same degrees
Hence it would be like
now we simplify the like terms
Hence
