Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
||
| Line 1: | Line 1: | ||
| − | What is the possible number of reflexive relations on a set of 5 elements? | + | What is the possible number of reflexive relations on a set of $5$ elements? |
(A) $2^{10}$ | (A) $2^{10}$ | ||
| Line 9: | Line 9: | ||
(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. | + | 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}} | ||
| Line 16: | Line 16: | ||
[[Category: GATE2010]] | [[Category: GATE2010]] | ||
[[Category: Sets and Relations questions]] | [[Category: Sets and Relations questions]] | ||
| + | [[Category:Mathematics Questions from GATE]] | ||
What is the possible number of reflexive relations on a set of $5$ elements?
(A) $2^{10}$
(B) $2^{15}$
(C) $2^{20}$
(D) $2^{25}$
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.
This work is licensed under the CC By-SA 3.0 , without all the cruft that would otherwise be put at the bottom of the page.
Sister Sites: GATE CSE Wiki, GATE CSE, Aptitude Overflow
GATECSE