Range of Relation \( R = \{(a, a^3)\} \)

📺 Video Explanation

📝 Question

Let relation \( R \) be defined as:

\[ R = \{(a, a^3) : a \text{ is a prime number less than } 5\} \]

Find the range of \( R \).

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✅ Solution

🔹 Step 1: Find Prime Numbers Less Than 5

Prime numbers less than 5 are:

\[ 2, 3 \]

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🔹 Step 2: Form Ordered Pairs

• \( a = 2 \Rightarrow (2, 2^3) = (2,8) \)
• \( a = 3 \Rightarrow (3, 3^3) = (3,27) \)

So,

\[ R = \{(2,8), (3,27)\} \]

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🔹 Step 3: Write Range

Range = set of second elements:

\[ \{8, 27\} \]

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🎯 Final Answer

\[ \boxed{\{8, 27\}} \]

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🚀 Exam Insight

• First identify restriction (prime numbers)
• Then apply function \( a^3 \)
• Range = second elements only