Question: 1. Prove by mathematical induction that for each positive integer n we have 131+351++(2n1)(2n+1)1=2n+1n 2. Consider the binary relation R={(x,y)x=y+1 or x=y1} on the set

1. Prove by mathematical induction that for each positive integer n we have 131+351++(2n1)(2n+1)1=2n+1n 2. Consider the binary relation R={(x,y)x=y+1 or x=y1} on the set all integers (a) Determine whether this relation is symmetric, reflexive, transitive, antisymmetric. (b) Is it an equivalence relation? Is it a partial or total ordering? 3. Let S={a,b,c,d} and let R be the binary relation on S corresponding to the matrix 1110111011100001

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