Suppose X = Rk+, for some k ≥ 2, and define x = (x1,...,xk) ≽ y = (y1,...,yk) if x ≥ y; that is, if for all l = 1, ..., k, xl ≥ yl. Show that ≽ is transitive but not complete

Q: (c) For the set A = {[0], [6]} ≤ Z12 determine the set U = h(A). Then for the set UC Z18 determine…

A: In group theory, sets like Z12​ and Z18​ are examples of cyclic groups under addition modulo 12 and…

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A: Suppose Its probability mass function is defined as,Where,

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A: Let An : = [ n ,∞)  where  n = 1,2, 3 .....  . So { An } n∈ℕ is an example of infinite collection…

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A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

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Q: 1]If 9:T>V and f:ST and gof IS injective, prove that both f añd 9 are injective.

A: Injective function:- for every x1=x2 implies that f(x1)= f(x2) .or vice versa.

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A: Given:

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A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

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A: Given:X={x=x1, x2, x3, x4 : xi∈1,2,3,4,5,6,7,8,9,10,11,12for i=1,2,3,4 such that…

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A: Given that .The objective, if then prove that .

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