- Study guides, Class notes & Summaries

Commutative Laws - ANS(1) A U B = B U A (2) A ∩ B = B ∩ A Associative Laws - ANS(1) A U (B U C) = (A U B) U C (2) A ∩ (B ∩ C) = (A ∩ B) ∩ C Distributive Laws - ANS(1) A U (B ∩ C) = (A U B) ∩ (C U A) (2) A ∩ (B U C) = (A ∩ B) U (C ∩ A) De Morgan's Laws - ANS(1) A U B (line over whole thing) = A ∩ B (lines over individual letters) (2) A ∩ B (line over whole thing) = A U B (lines over individual letters) Start a direct proof (P implies Q) - ANSassume ...

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5 pages

Written in 2022/2023

Grade A+

nighthawk117

A property of binomial coefficients - ANSC(n, k) + C(n, k+1) = C(n+1, k+1) Condition for C(n, k) + C(n, k+1) = C(n+1, k+1) - ANSn >= 0 Binomial Theorem - ANS(x + y)^n = sum( x^(n - k) y^k C(n, k) ) from k=0 to n Binomial Theorem conditions - ANSn >= 0 The division algorithm - ANSn =qd+r with 0 ≤ r <|d| and q and r are unique integers conditions for the division algorithm - ANSn, d integers and d is non-zero GCD-switching Theorem - ANSLet a,b,c,x ∈ Z and assu...

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4 pages

Written in 2022/2023

Grade A+

nighthawk117

Math 290 Final Exam Terms and Theorems (Analysis)|2024 perfect solution

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4 pages

Written in 2023/2024

Grade A+

Kylaperfect

Math 290 Final Exam Terms and Theorems (Analysis) Verified questions and answers|2024

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4 pages

Written in 2023/2024

Grade A+

kylaexcell

Math 290

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15 pages

Written in 2023/2024

Grade A+

EXCELINEXAMS

Math 290

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15 pages

Written in 2022/2023

Grade A+

NURSMARY

A ________________ ______________ in the variables a1x1 + ... + anxn = b where each ai and b are real numbers. - ANSlinear equation A linear equation in the variables a1x1 + ... + anxn = b where each ai and b are real numbers. We call the real numbers a1, ..., an the _____________ of the linear equation and the real number b the _____________ _________ of the linear equation. - ANScoefficients; constant term is 5x + 3y = 2 a linear equation? - ANSyes is 2x + 10y + 7z = 7 a lin...

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18 pages

Written in 2022/2023

Grade A+

nighthawk117

Set - ANSa collection of objects {1,2,3,4} Element - ANSan object in a set 1 is an element of {1,2} Boxes - ANSthink of brackets as boxes. For example {1,2,{3,4}}. The set {3,4} is contained in the set and is an element. However, 3 and 4 separately are not elements. N - ANSset of all natural numbers Z - ANSset of all integers Q - ANSset of all rational numbers R - ANSset of all real numbers Set builder notation - ANS{ 2x+1 : x E z} Empty Set - ANSThe set with not...

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4 pages

Written in 2022/2023

Grade A+

nighthawk117

Let A be a set and let P(A) denote the power set of A. If |P(AxA)| = 16 then |A|=4. - ANSFalse The statement P : for all integers "x", x>0 implies x^2 ≥ 0 is trivially true. - ANSTrue Let a,b,c,d,n be integers. If a+b congruent to c (mod n) and a+d congruent to c (mod n), then b is congruent to d (mod n). - ANSTrue Let n be an integer where n is congruent to 1 mod 4. Then n^12 is congruent to 1 mod 16 - ANSTrue Let P,Q,R be statements. Then Pˇ(QˆR)=(¬(Pˆ¬Q))ˆ(PˇR) -...

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3 pages

Written in 2022/2023

Grade A+

nighthawk117

Definition of a sequence - ANSA function from N to R epsilon definition of a limit - ANSFor all ε in R>0, there exists N element of R such that for all n element of natural numbers, n > N => |an - L| < ε What does "the limit of an equals L" mean? - ANS"The limit of an equals L" means that when n is large, an is near L. The definition weaves together the largeness and nearness so as to obtain a precise meaning. You tell me ______ . I'll tell you ______. You'll find...

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5 pages

Written in 2022/2023

Grade A+

nighthawk117

Proper Subset - ANSA subset different from the original set Cardinality - ANSThe number of elements in a set: |S| Universal set - ANSincludes all possible choices for a given set's elements Compliment - ANSAll elements in the Universal, except those in a given set Set - ANSA collection of elements (no repetition, order does not matter) Subset - ANSA set consisting of elements from a given set Statement - ANSA sentence with a truth value Logical connective - ANScombi...

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3 pages

Written in 2022/2023

Grade A+

nighthawk117

adjacent side - ANSthe side of a right triangle that touches the angle (not the hypotenuse) axis - ANSA horizontal or vertical line that establishes the relationship between data in a chart. axis of symmetry - ANSa line that divides a parabola in two equal halves and goes through the vertex bisector - ANScuts something into two equal parts circular - ANShaving the shape of a circle collinear - ANSpoints on the same line cosine - ANSratio of the adjacent side to the hypot...

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2 pages

Written in 2022/2023

Grade A+

nighthawk117

5-frame - ANS1.Direction 2. Distance 3. Time 4. Origin 5. Axis absolute value - ANSThe distance a number is from zero on a number line. ALWAYS POSITIVE algebra - ANSA mathematical phrase involving at least one variable and sometimes numbers and operation symbols. algebraic equation - ANSa number sentence that contains an equal sign and algebraic expressions - ex. y + 2 = 5 annual - ANShappening once a year associative - ANSthe grouping can change without changing the value ...

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12 pages

Written in 2022/2023

Grade A+

nighthawk117

What is a set? - ANSA collection of things. These things are called the elements of the set and they can be just about anything (pg. 3) Why are sets so important? - ANSBecause all of mathematics can be described with sets (pg. 3) What are elements? - ANSThe things that make up the set. They are separated by commas inside of braces (pg. 3) What is an infinite set? - ANSA set that has an infinite number of elements (pg. 3) What is a finite set? - ANSA set that has a finite number of el...

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25 pages

Written in 2022/2023

Grade A+

nighthawk117