CBSE Class 12 Sample Paper for 2021 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## How many reflexive relations are possible in a set A whose π(π΄) = 3.

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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^(ππ’ππππ ππ πππππππ‘π  ππ π΄ Γ π΄) = 2^(ππ’ππππ ππ πΈππππππ‘π  ππ π΄ Γ ππ’ππππ ππ πππππππ‘π  ππ π΄) = π^(π^π ) Now, Number of Reflexive Relations from A to A = 2^(ππ’ππππ ππ πΈππππππ‘π  ππ π΄ Γ π΄ π€βπππ π΄ Γ π΄ ππ  ππππππ₯ππ£π) = 2^(π^2 β π) Similarly Number of Symmetric Relations from A to A = 2^(ππ’ππππ ππ πΈππππππ‘π  ππ π΄ Γ π΄ π€βπππ π΄ Γ π΄ ππ  ππ¦ππππ‘πππ) = 2^(π(π + 1)) Now, Number of Reflexive Relations with 3 elements = 2^(π^2βπ) = 2^(3^2 β 3) = 2^(9 β 3) = π^π