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For the relation (R={(x,y):x-y\text{ is odd}}), where (x,y\in {1,2,3,4}), which statement is correct?संबंध (R={(x,y):x-y\text{ विषम है}}), जहाँ (x,y\in {1,2,3,4}), के लिए सही कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is symmetricसममित है
Step 1: If (x-y) is odd, then (y-x=-(x-y)) is also odd. Step 2: Hence whenever ((x,y)) is in the relation, ((y,x)) will also be in it. Step 3: In difference-based parity rules, changing the sign does not change oddness or evenness.चरण 1: यदि (x-y) विषम है, तो (y-x=-(x-y)) भी विषम होगा। चरण 2: इसलिए ((x,y)) होने पर ((y,x)) भी संबंध में होगा। चरण 3: अंतर वाले नियम में चिन्ह बदलने से सम या विषम होने की प्रकृति नहीं बदलती।
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