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

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

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.