Answer:
A ∩ B = {1, 3, 5}
A - B = {2, 4}
Step-by-step explanation:
The given problem regards sets and set notation, a set can simply be defined as a collection of values. One is given the following information:
A = {1, 2, 3, 4, 5}
B = {1, 3, 5, 6, 9}
One is asked to find the following:
A ∩ B,
A - B
1. Solving problem 1
A ∩ B,
The symbol (∩) in set notation refers to the intersection between the two sets. It essentially asks one to find all of the terms that two sets have in common. The given sets (A) and (B) have the values ({1, 3, 5}) in common thus, the following statement can be made,
A ∩ B = {1, 3, 5}
2. Solving problem 2
A - B
Subtracting two sets is essentially taking one set, and removing the values that are shared in common with the other set. Sets (A) and (B) have the following values in common ({1, 3, 5}). Thus, when doing (A - B), one will omit the values ({1, 3, 5}) from set (A).
A - B = {2, 4}
Answer:
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Yes y is directly proportional to x
Given:
If you divide any natural number n by 4, you get a remainder r.
To find:
The values of r if 
. Also find the domain and range.
Solution:
It is given that any natural number n by 4, you get a remainder r.
Where, n is a natural number, q is quotient, r is the remainder.
For 
,
So, 
.
For 
,
So, 
.
For 
,
So, 
.
For 
,
So, 
.
Therefore, the required value are 
if respectively.
The domain of the function is 
and the range of the function is 
.
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