-3x+42 + 4(x + (-15)) (no justification needed) =-3x + 42 + (4x + (-60)) =-3x + 42 + (-60 + 4x) =-3x + (42 + (-60)) + 4x =-3x + (-18) + 4x (no justification needed) =-3x + 4x + (-18) = (-3 + 4)x+ (-18) = 1x -18 (no justification needed) =x-18
-3x+42 + 4(x + (-15)) (no justification needed) =-3x + 42 + (4x + (-60)) =-3x + 42 + (-60 + 4x) =-3x + (42 + (-60)) + 4x =-3x + (-18) + 4x (no justification needed) =-3x + 4x + (-18) = (-3 + 4)x+ (-18) = 1x -18 (no justification needed) =x-18
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:-3x+42 + 4(x + (-15)) (no justification needed)
=-3x + 42 + (4x + (-60))
=-3x + 42 + (-60 + 4x)
=-3x + (42 + (-60)) + 4x
=-3x + (-18) + 4x (no justification needed)
=-3x + 4x + (-18)
= (-3 + 4)x+ (-18)
= 1x -18 (no justification needed)
=x-18
Transcribed Image Text:Properties 5.2.1: Properties of sets.
Let A be a set. Let a, b, and c be any numbers in the set A. Let # be an operation on numbers in the set.
• Closure property: The set A is closed under # if a #b is also in the set A for all a, b € A.
• Commutative property: The set A is commutative under # if a # b = b #a for all a, b € A.
• Associative property: The set A is associative under # if (a #b) # c = a # (b # c) for all a, b, c = A.
• Identity property: The set A has the identity property under # if a number exists in the set, called the identity, that leaves every
element unchanged under the operation.
• Inverse property: The set A has the inverse property under # if every number in the set has a corresponding number, called the
inverse, that results in the identity for A under the operation.
Another important property involving how a specific operation works with addition and subtraction is the distributive property.
• Distributive property: The operation # is left-distributive if a # (b±c) = a #c±a #c. The operation # is right-distributive if
(b + c) #a= b #a±c #a.
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