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What is the possible number of reflexive relations on a set of 5 elements?
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What is the possible number of reflexive relations on a set of $5$ elements?
 
 
 
(A) $2^{10}$
 
(A) $2^{10}$
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(D) $2^{25}$
 
(D) $2^{25}$
 
==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
 
==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
Consider a table of size 5*5 in which each possible pair is listed. In a reflexive relation, we must include  
+
Consider a table of size $5*5$ in which each possible pair is listed. In a reflexive relation, we must include  
all 5 diagonal elements. So from rest of the 20 elements, we have choice whether to include them or not. So we have $2^{20}$  
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all $5$ diagonal elements. From rest of the $20$ elements, we have choice whether to include them or not. Thus we have $2^{20}$  
 
possible reflexive relations. So option <b>(C)</b> is correct.
 
possible reflexive relations. So option <b>(C)</b> is correct.
 
{{Template:FBD}}
 
{{Template:FBD}}
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[[Category: GATE2010]]
 
[[Category: GATE2010]]
 
[[Category: Sets and Relations questions]]
 
[[Category: Sets and Relations questions]]
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[[Category:Mathematics Questions from GATE]]

Revision as of 12:24, 29 June 2014

What is the possible number of reflexive relations on a set of $5$ elements?

(A) $2^{10}$

(B) $2^{15}$

(C) $2^{20}$

(D) $2^{25}$

Solution by Happy Mittal

Consider a table of size $5*5$ in which each possible pair is listed. In a reflexive relation, we must include all $5$ diagonal elements. From rest of the $20$ elements, we have choice whether to include them or not. Thus we have $2^{20}$ possible reflexive relations. So option (C) is correct.



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What is the possible number of reflexive relations on a set of $5$ elements?

(A) $2^{10}$

(B) $2^{15}$

(C) $2^{20}$

(D) $2^{25}$

Solution by Happy Mittal[edit]

Consider a table of size $5*5$ in which each possible pair is listed. In a reflexive relation, we must include all $5$ diagonal elements. From rest of the $20$ elements, we have choice whether to include them or not. Thus we have $2^{20}$ possible reflexive relations. So option (C) is correct.



blog comments powered by Disqus