Asked by Dave
#1: a) Let a, b, c be integers and x is congruent to y (mod m). Prove that ax^2+bx+c is congruent to ay^2+by+c (mod m).
b) Show that the result in part a may be false if a, b, c are not all integers, even if ax^2+bx+c and ay^2+by+c are both integers.
#2: Let p: X --> Y and q: Y -->Z be functions such that (q(p)): X-->Z is onto. Prove that q is onto and give an example to show that p need not be onto.
#3: Give an algebraic proof to show that nCr = (n-1) C (r-1) + (n-1)C r.
These are a little bit confusing. I am stuck on these problems.
b) Show that the result in part a may be false if a, b, c are not all integers, even if ax^2+bx+c and ay^2+by+c are both integers.
#2: Let p: X --> Y and q: Y -->Z be functions such that (q(p)): X-->Z is onto. Prove that q is onto and give an example to show that p need not be onto.
#3: Give an algebraic proof to show that nCr = (n-1) C (r-1) + (n-1)C r.
These are a little bit confusing. I am stuck on these problems.
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