Class 11 Mathematics - Relations and Functions - Cartesian product of sets Easy Quiz

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यदि f:A→B एक फलन है, तो क्रमित युग्मों के समुच्चय के रूप में f किसका उपसमुच्चय होता है?

If f:A→B is a function, then, as a set of ordered pairs, f is a subset of which set?

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Correct Answer

A. A×B

Explanation

Simple Explanation

A से B में कोई भी संबंध A×B का उपसमुच्चय होता है, क्योंकि उसके प्रत्येक क्रमित युग्म का पहला अवयव A में और दूसरा अवयव B में होता है। फलन ऐसा विशेष संबंध है जिसमें A के प्रत्येक अवयव का B में ठीक एक प्रतिबिंब होता है। इसलिए f⊆A×B। परीक्षा-युक्ति: A से B के फलन में क्रम हमेशा domain से codomain की ओर होता है, इसलिए A×B चुनें, B×A नहीं। / Any relation from A to B is a subset of A×B because the first element of each ordered pair belongs to A and the second belongs to B. A function is a special relation in which every element of A has exactly one image in B. Hence, f⊆A×B. Exam tip: For a function from A to B, the order is domain first and codomain second, so choose A×B rather than B×A.

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