If X, Y, Z ER and x≤Z, show that XL Y S z if and only if |x-y| + | y-z| = |x-z). Interpret geometrically.

Q: Let P (m, n) be the statement “m divides n," where the domain for both variables consists of all…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: Define nullspace.

A: We have to define, what is null space.

Q: Let u = , v = , and w = . find uw

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Q: Find the mid point for A( 1 , 2 ) B( 7, 8 )

A: Mid-point for the given points is- a=x1+x22,b=y1+y22 where a & b are the mid-points, and,…

Q: Find a relationship between x,y and z with reasons

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Q: let à = (3,4,5) and To (5,2, 6) a Find (2-6) x (a+b)

A: We need to find out the cross product.

Q: Z

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Q: let a1 is (-3,2,6) a2 is (-9,-7,-2) and b is (-18,-27,-23). Is b in the span of of a1 and a2

A: The objective of this question is to determine whether the vector b is in the span of vectors a1 and…

Q: Show that if a > b, and a, b i= 0, then b- 1 > a - 1, provided that a and b have the same…

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Q: Show that a group G of order par for district primes p and q is solvable

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Q: Let U=(-4, 3, 3) and V=(2, 1, 1). Find (2U+V), *. | (then find | (2U+V

A: Find 2U+V and it's magnitude.

Q: Provide an interpretation which is true and one that is false. (∃ x)(P(x,b))

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Q: uxv is , and U x u is

A: We are asked to find the cross product of the vectors

Q: If the composition p ∘ u = (2-y, 2-x), show that the fixed points are the points on the line y =…

A: The objective of this question is to prove that the fixed points of the composition function p ∘ u =…

Q: If A = {(x, y): (2, -2), (4, -1), (6, 0), . . .}, complete the rule for set A. y= 1/2x - 3 -1/2x -…

A: Observe the given pattern of set A then complete the rule.

Q: Let u= and v= identify 3u+v???

A: We have to identify 3u+v for the given vectors: u=2, -3 and v=4, -1. Finding 3u: 32, -3=6, -3

Q: Is X and Y are independent

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Q: Let A = {j, z}, B = {1,5,7}. Each element is expressed as an ordered pair. ВХА3{ }

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Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: Let ū = (3, – 4, – 10) and i = (– 7, – 2, 0). - 2ü + 20 (-8,-12 - 20)

A: Given :-  u=<3,-4,-10>  v=<-7,-2,0>  To find:-  2u+2v

Q: 5. State the domain and range of each function. a) y = 2x- 1 b) y = -3(x – 4)² + 1 c) y d) y = V-3(x…

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Q: If xly, then show that ||x+ y|| = ||x- y|!.

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Q: 3) Let x = (-1,3,2,-4), and y = (1,0,2,3). Find the following distances || x = || = ? []x - || =?

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Q: let u = <1, 2, 2> , v = <1, -1, -1>, w = <1, 3, -1> , and z = <2, 11, 8>.…

A: Given: u1 is parallel to u, u2 is parallel to v, and u3 is parallel to w.So, u1= au , u2=bv and…

Q: given u = and v= find u*v

A: To find out the dot product u*v

Q: Find the value of X such that and are perpendicular

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Q: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…