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roster method is just like listing method
my math teacher says no but i think that there is a pattern
meaning of proper subsets
For a set with n members, there are 2n possible subsets; thus the set {1, 2, 3, 4, 5, 6, 7, 8, 9} has 9 members and 29 = 512 possible subsets.
Number of subsets with no members = 1
Number of subsets with one member = 5.
Number of subsets with 2 members = (5 x 4)/2 = 10.
Number of subsets with 3 members = (5 x 4 x 3 /(3 x 2) = 10.
Number of subsets with 4 members = (5 x 4 x 3 x 2)/(4 x 3 x 2) = 5.
Number of subsets with 5 members = 1
Total subsets = 1 + 5 + 10 + 10 + 5 + 1= 32.
A set with n elements has 2n subsets. In this case n = 5 and 25 = 32.
The proof in the case that n = 5 uses a basic counting technique which say that if you have five things to do, multiply together the number of ways to do each step to get the total number of ways all 5 steps can be completed.
In this case you want to make a subset of {1,2,3,4,5} and the five steps consist of deciding for each of the 5 numbers whether or not to put it in the subset. At each step you have two choices: put it in or leave it out.
Cardinality is simply the number of elements of a given set. You can use the cardinality of a set to determine which elements will go into the subset. Every element in the subset must come from the cardinality of the original set. For example, a set may contain {a,b,c,d} which makes the cardinality 4. You can choose any of those elements to form a subset. Examples of subsets may be {a,c} {a, b, c} etc.
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16
All multiples MUST be multiples of 4.
{}, {1}, {2} and {1,2}
Sets contain elements. The intersection of sets (represented by an upside-down 'U') is the list of elements that are common in both sets. The union of sets (represented by 'U') is the list of all the elements in the relevant sets.
E.g. If A={a,b,c,d,e,f} and B={a,e,i,o,u}:
The intersection of A and B is {a,e}.
The union of A and B is {a,b,c,d,e,f,i,o,u} (notice how repeating elements, e.g. 'a' and 'e', are only listed once even though they occur in both sets.)
They are the infinite number of rational numbers between 0 and +6
1 mile = 5280 feet
24816 feet = 24816/5280 miles = 4.7 miles
Monday, Tuesday, Wednesday, Thursday, and Friday are called the weekdays. They are the days on which it is customary to work.
J. M. G. Gradidge has written:
'Clothes moths and carpet beetles' -- subject(s): Carpet beetles, Clothes moths
Anything less than -6 is -5, - 4, -3, -2, -1 and all positive numbers.
1,3,5,7,9
