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How many non zero entries does the matrix representing relation $R$ on a set $A$ = $\left \{ 1,2,3,4,5,6....1000 \right \}$.

  • a. $R = \left \{ (x,y) \; | x = y \pm 1 \right \}$
  • b. $R = \left \{ (x,y) \; | x + y = 1000 \right \}$
asked in Set Theory & Algebra by Veteran (45.6k points)   | 62 views

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A. R = { (1,2),(2,3),(3,4),...,(n-1,n) } Union Reverse of former.

Total combinations = 2*(n-1) = 1998.

B. R = = { (1,n-1),(2,n-2),(3,n-3),...,(n-1,1)

Total combinations = n-1 = 999.
answered by Loyal (3.2k points)  
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