For A = {x|x is an integer greater than 7} and B = {x|x is an integer less than or equal to 12}, determine A∩B and A∪B.

A∩B =
{x|x is an integer greater than 7} and {x|x is an integer less than or equal to 12}=
{x|x is an integer greater than 7 and less than or equal to 12}


A∪B =
{x|x is an integer greater than 7} or {x|x is an integer less than or equal to 12}=
all integers

True or false: {16, 17, 18, 19}=[16,19] ?

False. The interval [16,19] contains all the number beginning at 16 and ending at 19 while the set {16, 17,  18, 19} only includes the four integers.

True or false: {16, 17, 18, 19} is a subset of (16,19) ?

False. The interval (16,19) does not include 16 and 19.

True or false: {16, 17, 18, 19} is a subset of [16,19] ?

True. The interval [16,19] contains all the numbers between and including 16 and 19.

How do you write a set In a roster for and in set-builder notation

The names of the formats are self explanatory - which is a common practice in math. Roster form is a listing of elements whereas set-builder notation is a way of describing what elements are in a set. If a set has elements that cannot be listed completely then set builder notation is a viable option. 
Suppose E1 is the set of even numbers between 2 and 12 then either form will work: 
E1={4,6,8,10}={n: 2|n and 2 < n < 12} 
Now let E2 be the even number between 2 and 12,000,000,000. Roster form is really no longer practical - and this isn't even an infinite set. So we use builder notation. 
E2={n: 2|n and 2 < n < 12*10^9}

If f is chosen at random from the set {2, 3, 4} and m is chosen at random from the set {9, 10, 11}, what is the probability that f is a factor of m?

U={2, 3, 4}x{9, 10, 11} 

and n(U)=9 


from which E = {(2,10), (3,9)} 


and so n(E)=2 

p=n(E)/n(U)=2/9

Find A∩B if A={6,3,10,12,2} and B={10,7,-3,12}

A∩B=
{6,3,10,12,2}∩{10,7,-3,12}=
{10,12}

Let U = {1,2,3,4,5,6,7,8} A = {1,2,3,4,5,7} B = {2,3,5,6} Determine A U B

A U B =
{1,2,3,4,5,7} U {2,3,5,6}=
{1,2,3,4,5,6,7} 

:)

Why are the infinite sets: set of natural numbers, set of integers, set of odd numbers and set of even numbers equal? Prove it.

These sets are not equal. We call them equivalent (isomorphic) because they have the same number of elements. The proof is that we can find a bijection between the natural numbers and each other set. Please search for examples on your own - it's not too tough 

:)

List all the possible subsets of B={2,4,6,8,10}

The number of subsets of a set of n elements is 
 
there are 32: 
{} 
{2}
{4}
{6}
{8}
{10} 
{2,4}
{2,6}
{2,8}
{2,10}
{4,6}
{4,8}
{4,10}
{6,8}
{6,10}
{8,10} 
{2,4,6}
{2,4,8}
{2,4,10}
{2,6,8}
{2,6,10}
{2,8,10}
{4,6,8}
{4,6,10}
{4,8,10}
{6,8,10} 
{2,4,6,8}
{2,4,6,10}
{2,4,8,10}
{2,6,8,10}
{4,6,8,10} 
{2,4,6,8,10} 

If A = {2, 4, 6, 8, 10…} and B = {1, 3, 5, 7, …}, what is A ∩ B?

The intersection of two disjoint sets is the empty set

assume that power set of A equal to power set of B.then A=B.

This is not true: 
A= {1, 2} 
B= {4, t} 
have 

 

but 

 

(two sets are equal if they have exactly same elements) 

:)

Given sets A = {1, 3, 7}, B = {1, 3, 5, 9}, what is the union of A and B?

 A = {1, 3, 7}
 B = {1, 3, 5, 9}

The union is the set of all elements that belong to either set A or set B or both:

 A∪B={1,3,5,7,9}

Find the domain and range.

Find the domain and range.
R={( -4, -7), ( 12, 5), ( 11, -9), ( 11, -3)}


Solution:

The domain of a relation is the set of all first coordinates so we can write Dom R={-4, 12, 11}

The range of a relation is the set of all second coordinates so we can write Ran R={-7, 5, -9, -3}