Question 12 of 33beginner🔧 ApplyShort Answer2 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 6)
For More Understanding

Explanation

This question tests understanding of relations, roster form, domain and range. Following the pattern in Example 7 of the context, we substitute each valid x value into the equation y = x + 5. Since x is a natural number less than 4, x takes values 1, 2, 3. The corresponding y values are 6, 7, 8 respectively. The domain consists of all first elements of 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 y for each x: For x=1, y=6; for x=2, y=7; for x=3, y=8

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

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

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

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