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| − | 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) $2^{10}$ | ||
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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. | + | 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: | + | [[Category: Sets and Relations 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.
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. So from rest of the 20 elements, we have choice whether to include them or not. So we have $2^{20}$ possible reflexive relations. So option (C) is correct.
GATECSE