If x, y, z are integer's numbers then: 1) Show that if x \y then x \yz 2) By use part 1 show that if x\y and x\z then x\ym - zn for m, ne Z

Q: Write a proof that proves the Union Un an element of natural numbers (-1/n, 2-1/n)=(-1, 2). Also…

A: The given interval is (-1/n,2-1/n) where natural number n belongs to positive integers. So that we…

Q: Find all possible digits that can be placed in the space so that the numbers is 1,182,1_4

A: Apply the rule for a number divisible by 9.

Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x \ ym – zn for m, n e Z…

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Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

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Q: 1. Simplify the following expressions: a) (x– 1)(x+ 2) b) (х- 10) - (х — 2) c) 4(x – 1)(x+ 1) + 2(x…

A: topic - simplification

Q: А Q(1, 1) в Q(2, 0) vyQ(1, y) 3xQ(x, 2)

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Q: 1 2 5. 2 . 5 +1. Va) da Find + C

A: Given: I=∫-5·x6+1x-2x6+1·xdx We know that; The Sum rule; ∫fx±gxdx=∫fxdx±∫gxdx The Power rule;…

Q: Show that if x+yi=(a+bi)- is true, then x-yi=(a-bi)-is all real numbers). true (x, y, a, and b are

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Q: 8. Let a, b and c be any positive real numbers. Prove that b² + c² a²+b² 2c a² + c² + 2b 2a > a+b+c.

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Q: Suppose x and y are integers. Show that If x y, then x | 3y - y + 5y. 1) What is your assumption? 2)…

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Q: If a(3, 4) – b(2, 4) = (8, 10), determine a and b.

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Q: -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 a) x-525 b) x-5 5

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Q: 1 금sin-1를 +C True False

A: We have to check

Q: Determine if the following are true or false: a) 4C1, 4) b) 4E[1, 4) c) (4)C (1, (4)]

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Q: EIf a,,a,,a,.--,a, be an A P of non - zero terms, prove that ------ 1 1 +. 1 n-1 %3D a,a, a,a, a,a,

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Q: Which of the following is the graph of (y-2)² = −4(x - 2)² 12 5 n 24 X + 3 24 CV 9 T ny 7 T O & 7 6…

A: (y-2)2 = -4(x-2) compare with equation   (y-k)2 = – 4a(x-h) so we get   k = 2 h = 2 a = -1

Q: 10 If A= 20 20 20 o and B –201 40 -20! -10. Find: а) А+В b) A-B с) А.В

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Q: Prove that ord,(a + b) > min(ord,a, ord,b) with equality holds if ord,a ± ord,b.

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Q: Prove the following logical expression: x*y + x*y' = x

A: The expression xy + xy' = x is of Boolean algebra Taking Left hand side xy + xy'

Q: (7) For any nonzero a, b € Z, the gcd(a, b) divides the lem(a, b). (8) If r, y € Z and 3 divides ry,…

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Q: Write Dual: minZ= 40x, +120x s.t *1+4x2= 4 2x +3x225 Xg.X20. C=40 120]

A: follow second step

Q: Decide whether the equation is an identity or a contradiction. 4) 4(4x+ 6) 16x + 24 A) Contradiction…

A: we have to decide whether the equation is an identity or a contradiction. 44x+6=16x+24

Q: Find the dual of the statement (xy¯¯¯)+(x¯¯¯z)

A: To find the dual of statement , we replace • by + and + by •

Q: 28) 28) -4 < xs -2 A) (-4, -2) B) (-4, -2] C) [-4, -2) D) [-4, -2]

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Q: Prove A X (BUC) - (Ax B) U (A x C)

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Q: 19) If A = {p, m} and B= {3, 6, 4} %3D Find B XA (Use proper notation)

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Q: 1. Determine whether or not the expressions below are wff (well-formed formulae). Explain your…

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Q: Find values of x and y in order to make the following

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Q: Show that there is exactly one real number t such that eTt + te" 207 + V2021.

A: Let us take an equation: g(x)=t Where g(x) be any function of x In order to show existence of x such…

Q: V5 -V3 V5 + V3 Simplify the following expression: A) 4+ v15 B) 4- V15 c) 8 + V8 (D) 8 - V8 Question…

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Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: 1) 2*•23 - 25 2) 2* = 2 3) 4) x+y=-3 5) 24 • 2* = 26 6) 2* • 2 = 23

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Q: Let S be the set of numbers of the form { ((-1)^(n + 1)) (n - 1)/(n + 1) } where n is an element of…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.