Class 12 Mathematics - Relations and Functions - Relations Medium Quiz

Mathematics Relations and Functions Relations Medium Class 12 Level 29

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Question 1/1 Medium Mathematics Relations and Functions Binary operations Class 12 Level 29

यदि \(S=\{0,1,2,3\}\) पर संक्रिया (a*b) को (a*b=(a+b)) का (4) से भाग देने पर शेषफल माना गया है तो क्या यह संक्रिया (S) पर बंद है?

If the operation (a*b) on \(S=\{0,1,2,3\}\) is defined as the remainder when (a+b) is divided by (4), then is this operation closed on (S)?

Explanation opens after your attempt
Correct Answer

A. हाँ क्योंकि हर परिणाम (S) में हैYes because every result belongs to (S)

Step 1

Concept

बंद संक्रिया में हर \(a,b \in S\) के लिए \(a*b \in S\) होना चाहिए। / For closure, (a*b) must belong to (S) for all \(a,b \in S\).

Step 2

Why this answer is correct

(4) से भाग देने पर शेषफल हमेशा (0,1,2,3) में से एक होगा। / The remainder on division by (4) is always one of (0,1,2,3).

Step 3

Exam Tip

परीक्षा में शेषफल वाली संक्रिया में संभावित शेषफलों को समुच्चय से मिलाकर देखें। / In exams, compare the possible remainders with the given set.

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