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In Class 12 Mathematics, under Relations and Functions, students learn that a relation R on a set A is symmetric when (a, b) ∈ R always implies (b, a) ∈ R for every a, b ∈ A. They practise checking this condition from ordered pairs, rosters, mappings, and relation statements, and identify examples such as equality and sibling relationships. The topic also helps them distinguish symmetric relations from relations such as “less than” and apply the concept while studying properties of relations.
Easy · Level 7 · 1 questions
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Question 1EasyLevel 7
The relation (R={(a,b):a-b\text{ is even}}) is given on integers. What is it?संबंध (R={(a,b):a-b\text{ सम है}}) पूर्णांकों पर दिया है। यह कैसा है?
Correct answer:सही उत्तर:A
Step 1: If (a-b) is even, then (b-a=-(a-b)) is also even. Step 2: Therefore, whenever ((a,b)) satisfies the condition, ((b,a)) also satisfies it. Step 3: In parity questions, remember that the negative of an even number is also even.चरण 1: यदि (a-b) सम है, तो (b-a=-(a-b)) भी सम होगा। चरण 2: इसलिए ((a,b)) होने पर ((b,a)) भी शर्त पूरी करता है। चरण 3: सम-विषम से जुड़े प्रश्नों में ऋणात्मक सम संख्या भी सम ही रहती है।
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