(a) By contradiction, prove that V x, y € Z, if xy is even and y is odd then x is even. (b) Show that the set is countable. 3' 3'9' 6 (c) Find the values of x and y for which (x + y, 0) = (3, x – y)

Q: Method of algebra and cite a property used for every step: (Z − Y) − (Y − X) = Z − Y.

A: To prove: (Z − Y) − (Y − X) = Z − Y

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A: Let's find.

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A:

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A:

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A: Step 1: proof  let (A/C)∩(B/C)∩(A/B)=Φ this means ∃x∈(A/C)∩(B/C)∩(A/B) Step 2:⇒x∈A/C,x∈B/C,x∈A/B…

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A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: (a) [0, 1] (c) {2,7} (e) {÷ :n e N} (g) [0, 1] U [2, 3] (b) (0, 1) (d) {T,e} (f) {0}

A: To find supremum of given sets .

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A: As per the guideline, I am supposed to solve only first question from the given problems.Given that…

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A: Given that x>0 and y>0, then to prove that xy>0. x, y are integers.

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A: This question is from MATLAB. We'll run the given commands and get the result as solution.

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A: Using the properties of covariance, the expression simplifies to:cov(a + bX, c + dY) = ac * cov(X,…

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A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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A:

Q: Û Jolve T he Set of inear eguation -7X,-4X2-X3= ) -lo x, -57, -2X-3

A: Here I am attaching image so that you understand each and every step.

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Q: (a) By contradiction, prove that Vr, y € Z, if ry is even and y is odd then x is even. (b) Show that…

A:

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: The maximum value of function  f(x,y,z)=(xyz)13such that  x,y,z are non negative  and x+y+z=8

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A:

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A: According to the Bartleby Guidelines, we can answer only first three subparts of a question at a…

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A: Show that if P(A) &gt; 0 thenP(AB|A) &gt; P(AB|AUB)

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A: GIVEN

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A: Let us assume X1 denotes {1,2} faces show in 10 throw . The probability of that will be P(X1=1 and…

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A: