CBSE Class 12 Sample Paper for 2021 Boards

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Question 1 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by

How many reflexive relations are possible in a set A whose 𝑛(𝐴) = 3.

How many reflexive relations are possible in a set A whose n(A) = 3

Question 1 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

 

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Question 1 (Choice 2) How many reflexive relations are possible in a set A whose 𝑛(𝐴) = 3. Number of Relations from A to A = 2^(π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘’π‘™π‘’π‘šπ‘’π‘›π‘‘π‘  𝑖𝑛 𝐴 Γ— 𝐴) = 2^(π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ πΈπ‘™π‘’π‘šπ‘’π‘›π‘‘π‘  𝑖𝑛 𝐴 Γ— π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘’π‘™π‘’π‘šπ‘’π‘›π‘‘π‘  𝑖𝑛 𝐴) = 𝟐^(𝒏^𝟐 ) Now, Number of Reflexive Relations from A to A = 2^(π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ πΈπ‘™π‘’π‘šπ‘’π‘›π‘‘π‘  𝑖𝑛 𝐴 Γ— 𝐴 π‘€β„Žπ‘’π‘Ÿπ‘’ 𝐴 Γ— 𝐴 𝑖𝑠 π‘Ÿπ‘’π‘“π‘™π‘’π‘₯𝑖𝑣𝑒) = 2^(𝑛^2 βˆ’ 𝑛) Similarly Number of Symmetric Relations from A to A = 2^(π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ πΈπ‘™π‘’π‘šπ‘’π‘›π‘‘π‘  𝑖𝑛 𝐴 Γ— 𝐴 π‘€β„Žπ‘’π‘Ÿπ‘’ 𝐴 Γ— 𝐴 𝑖𝑠 π‘†π‘¦π‘šπ‘šπ‘’π‘‘π‘Ÿπ‘–π‘) = 2^(𝑛(𝑛 + 1)) Now, Number of Reflexive Relations with 3 elements = 2^(𝑛^2βˆ’π‘›) = 2^(3^2 βˆ’ 3) = 2^(9 βˆ’ 3) = 𝟐^πŸ”

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo