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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

DM - Grand Test -Q13


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+1 vote

Let S be a set of 12 elements. Let a, b be two different specific elements of S i.e. a,b \in S and let 2^S denote the set of all subsets of set S. Then |\{x:x\in 2^S \text{ and } a,b \in x\}| is ________?

asked Aug 30, 2020 by gbeditor-2 (72,840 points)
reshown Aug 31, 2020 by gbeditor-2

2 Answers

+1 vote
 
Best answer
10C0 + 10C1 + ................+10C10 = 2^10 = 1024
answered Sep 7, 2020 by prashantpro19 (970 points)
selected Sep 7, 2020 by deepak-gatebook
0 votes

Since a and b are specific two different elements, so,  |\{x:x\in 2^S \text{ and } a,b \in x\}|  means the number of subset of S which contain both a,b. So, a,b must be in the subset, and remaining 10 elements have choice of being in or not in the subset, so, we have  2^10 such subsets. 

 

answered Sep 7, 2020 by deepak-gatebook (226,240 points)
Answer:

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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
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