Question 15 of 35beginner🔧 ApplyShort Answer2 marks

Determine the domain and range of the relation RR defined by R={(x,x+5):x∈{0,1,2,3,4,5}}R = \{(x, x + 5) : x \in \{0, 1, 2, 3, 4, 5\}\}.

Correct Answer

Given the relation R={(x,x+5):x∈{0,1,2,3,4,5}}R = \{(x, x + 5) : x \in \{0, 1, 2, 3, 4, 5\}\}. To find the domain and range, we first express the relation in roster form by substituting the values of xx from the given set.

By substituting x=0,1,2,3,4,5x = 0, 1, 2, 3, 4, 5, we get the ordered pairs: R={(0,5),(1,6),(2,7),(3,8),(4,9),(5,10)}R = \{(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)\}.

The domain of a relation is the set of all first elements of the ordered pairs. Therefore, the domain of RR is {0,1,2,3,4,5}\{0, 1, 2, 3, 4, 5\}. The range of a relation is the set of all second elements of the ordered pairs. Therefore, the range of RR is {5,6,7,8,9,10}\{5, 6, 7, 8, 9, 10\}.

Exercise: EXERCISE 2.2 | Q: 6 | (Page 7)
For More Understanding

Explanation

The solution follows the method illustrated in Example 8 and Exercise 2.2 Question 1 of the textbook. To determine the domain and range, the relation is first converted from set-builder form to roster form. The domain consists of the first components (xx values) of the ordered pairs, which corresponds to the set provided in the definition. The range consists of the second components (yy values), calculated as x+5x + 5 for each element in the domain.

Solution Steps

  1. Step 1: Identify the values of xx from the given set {0,1,2,3,4,5}\{0, 1, 2, 3, 4, 5\}.

  2. Step 2: Calculate the corresponding second element y=x+5y = x + 5 for each xx.

  3. Step 3: Write the relation in roster form: R={(0,5),(1,6),(2,7),(3,8),(4,9),(5,10)}R = \{(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)\}.

  4. Step 4: Identify the domain as the set of first elements: {0,1,2,3,4,5}\{0, 1, 2, 3, 4, 5\}.

  5. Step 5: Identify the range as the set of second elements: {5,6,7,8,9,10}\{5, 6, 7, 8, 9, 10\}.

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