1) Let \( s=\{1,2,3,4,5,6,7,8,9\} \) Detumine whethex or not each of the following is a partition of \( S \). i) \( \{21,3,5\},\{2,6\},\{4,8,9\}\} \) ii) \( \{\{1,3,5\},\{2,4,6,8\},(\{5,7,9\}\} \) 2) find the power set of the set \( A\{\alpha, \beta, \gamma\} \) 3) Let \( A=\{1,3,5,7,9\}, B=\{2,4,6,8\} \) \( R=\{3,2),(5,2),(5,4),(7,2),(7,4) \), \( (7,6),(9,2),(9,4),(9,6),(9,8)\} \) find i) Determine the matrix of the relation ii) Draw the anow diagram of \( R \) iii) Find inverse relation \( R^{-1} \) of \( R \) iv) Determine the domain and range of \( R \). 4) Determine whether following relation are symmetric, asymmetric and antisymmattic \[ \left[\begin{array}{lll} 1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \end{array}\right] \] 5) Let \( A=\{a, b, c\} \) and let \( M_{R}=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & 1 & 1\end{array}\right] \) Determine whether \( R \) is an equivalence relation.
Added by Raveena K.
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