Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Question
Chapter 75, Problem 9A
To determine
(a)
The value of angle of rotation
To determine
(b)
The value of angle of tilt
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7.
Suppose that X is a set, that I is a nonempty set, and that for each i Є I that Yi
is a set. Suppose that I is a nonempty set. Prove the following:2
(a) If Y; CX for all i EI, then Uiel Yi C X.
¹See Table 4.8.1 in zyBooks.
Recall:
Nie X₁ = Vi Є I (x = X₁) and x = Uier X₁ = i Є I (x Є Xi).
(b) If XCY; for all i Є I, then X Ciel Yi.
(c) U(x)=xnUY.
iЄI
ΕΙ
8.
For each of the following functions, determine whether or not it is (i) injective
and/or (ii) surjective. Justify why or why not.
(a) fiZZ defined by fi(n) = 2n.
(b) f2 RR defined by f2(x) = x² − 4x+7.
:
(c) f3 Z {0, 1} defined by f3(n) = 0 if n is even and f3(n) = 1 if n is odd.
(d) f4 Z N defined by f4(n) = 2n if n > 0 and f4(n) = -2n-1 if n < 0.
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Mathematics For Machine Technology
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