Question 12 of 35beginner🔧 ApplyShort Answer3 marks

Define a relation RR on the set NN of natural numbers by R={(x,y):y=x+5,x is a natural number less than 4;x,y∈N}R = \{(x, y) : y = x + 5, x \text{ is a natural number less than } 4; x, y \in N\}. Depict this relationship using roster form. Write down the domain and the range.

Correct Answer

Roster form: R = {(1, 6), (2, 7), (3, 8)}

Domain: {1, 2, 3}

Range: {6, 7, 8}

Exercise: EXERCISE 2.2 | Q: 2 | (Page 7)
For More Understanding

Explanation

This question tests understanding of relations, roster form, domain and range. The relation is defined by y = x + 5 where x is a natural number less than 4. Since natural numbers N = {1, 2, 3, ...}, the values of x less than 4 are 1, 2, and 3. Substituting these values gives the ordered pairs (1, 6), (2, 7), and (3, 8). The domain consists of all first elements of the ordered pairs, and the range consists of all second elements.

Solution Steps

  1. Step 1: Identify values of x: Natural numbers less than 4 are x = 1, 2, 3

  2. Step 2: Calculate corresponding y values using y = x + 5: When x = 1, y = 6; when x = 2, y = 7; when x = 3, y = 8

  3. Step 3: Write in roster form: R = {(1, 6), (2, 7), (3, 8)}

  4. Step 4: Domain = {1, 2, 3} (set of first elements)

  5. Step 5: Range = {6, 7, 8} (set of second elements)

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