यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{1,2,3,4,5,6\}\) और \(R=\{(a,b):a+b=7\}\) है, तो (R) के कितने उपसमुच्चय कम से कम एक युग्म रखते हैं जिसका पहला अवयव (1) है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{1,2,3,4,5,6\}\), and \(R=\{(a,b):a+b=7\}\), how many subsets of (R) contain at least one pair whose first component is (1)?
Explanation opens after your attempt
Correct Answer
B. (32)
Concept
There are (6) pairs in (R), and only ((1,6)) has first component (1). It must be included, so the other (5) pairs are free, giving \(2^5=32\).
Why this answer is correct
The correct answer is B. (32). There are (6) pairs in (R), and only ((1,6)) has first component (1). It must be included, so the other (5) pairs are free, giving \(2^5=32\).
Exam Tip
(R) में (6) युग्म हैं और पहला अवयव (1) वाला केवल ((1,6)) है। उसे रखना होगा, इसलिए बाकी (5) युग्म स्वतंत्र हैं और संख्या \(2^5=32\) है।
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