Math Problem Statement

let A = {- 2, - 1, 0, 1, 2} and B = {0, 1, h, 9} , let R={(2,4). (-1,1), (0,0),(1) (2.4)3

find dom (R), Range (R), (6-dom (R)

Solution

We are given:

  • Set A={2,1,0,1,2}A = \{-2, -1, 0, 1, 2\}
  • Set B={0,1,h,9}B = \{0, 1, h, 9\}
  • Relation R={(2,4),(1,1),(0,0),(1),(2.4)3}R = \{(2,4), (-1,1), (0,0), (1), (2.4)3\}

There seems to be some confusion with the formatting of relation RR. I'll assume it's intended to be:

R={(2,4),(1,1),(0,0)}R = \{(2, 4), (-1, 1), (0, 0)\}

Let’s now proceed with the calculations:

1. Domain of RR:

The domain of RR is the set of all the first elements of the ordered pairs in RR.

So, the domain of RR is: Dom(R)={2,1,0}\text{Dom}(R) = \{2, -1, 0\}

2. Range of RR:

The range of RR is the set of all the second elements of the ordered pairs in RR.

So, the range of RR is: Range(R)={4,1,0}\text{Range}(R) = \{4, 1, 0\}

3. 6Dom(R)6 - \text{Dom}(R):

Now, to compute 6Dom(R)6 - \text{Dom}(R), we subtract each element of the domain from 6: 6Dom(R)={62,6(1),60}={4,7,6}6 - \text{Dom}(R) = \{6 - 2, 6 - (-1), 6 - 0\} = \{4, 7, 6\}

Summary:

  • Domain: {2,1,0}\{2, -1, 0\}
  • Range: {4,1,0}\{4, 1, 0\}
  • 6Dom(R)={4,7,6}6 - \text{Dom}(R) = \{4, 7, 6\}

Let me know if you'd like further details or explanations.

Here are five related questions you can explore:

  1. What is the domain and range of the relation R={(2,3),(1,4),(0,5)}R = \{(-2, 3), (1, -4), (0, 5)\}?
  2. How do you determine if a relation is a function?
  3. Can the domain of a relation contain repeated values?
  4. How do you represent a relation using a matrix?
  5. How do you find the inverse of a relation?

Tip: Always ensure that relations are written clearly to avoid confusion with their elements and structure.

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Math Problem Analysis

Mathematical Concepts

Sets
Relations
Domain and Range

Formulas

Domain: Set of first elements in ordered pairs
Range: Set of second elements in ordered pairs
6 - Dom(R): Subtraction of domain elements from 6

Theorems

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Suitable Grade Level

Grades 9-12