How many reflexive relations are possible in a set A whose π(π΄) = 3.
CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
Last updated at April 16, 2024 by Teachoo
Question 1 (Choice 2) How many reflexive relations are possible in a set A whose π(π΄) = 3. Number of Relations from A to A = 2^(ππ’ππππ ππ πππππππ‘π ππ π΄ Γ π΄) = 2^(ππ’ππππ ππ πΈππππππ‘π ππ π΄ Γ ππ’ππππ ππ πππππππ‘π ππ π΄) = π^(π^π ) Now, Number of Reflexive Relations from A to A = 2^(ππ’ππππ ππ πΈππππππ‘π ππ π΄ Γ π΄ π€βπππ π΄ Γ π΄ ππ ππππππ₯ππ£π) = 2^(π^2 β π) Similarly Number of Symmetric Relations from A to A = 2^(ππ’ππππ ππ πΈππππππ‘π ππ π΄ Γ π΄ π€βπππ π΄ Γ π΄ ππ ππ¦ππππ‘πππ) = 2^(π(π + 1)) Now, Number of Reflexive Relations with 3 elements = 2^(π^2βπ) = 2^(3^2 β 3) = 2^(9 β 3) = π^π