Recent content by mbcsantin

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    Is the Induction Hypothesis n^2 - n + 41 Prime for All Natural Numbers?

    Homework Statement For all n is an element of N, n2 - n + 41 is prime N= natural numbers Homework Equations None. The Attempt at a Solution Let n=1 12 - 1 + 41 = 41 is prime. n2 - n + 41 is not prime. so this hypothesis is not correct. assume n2 - n + 41 is not prime...
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    Prove/Find Counterexample: Intro to Set Theory

    But what if I use the element proof for this.. Supposed that A is a subset of B. Let x is an element of A u C. therefore, x is an element of A and x is an element of C. Since A is a subset of B by the definition of containment, x is an element of B. Since x is an element of B and x is...
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    Undergrad Igma notation 2i-1 = 2n, for all n is an element of N

    Here is my attempt at this problem: n sigma notation 2i-1= 2n, for all n is an element of N i=1 n=1 1 sigma notation 21-1= 20 = 1 not equal to 21 i=1 n=1 is an element of N Hence, n sigma notation 2i-1=2n doesn't hold for all n is an element of N i=1 did i do this right?
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    Undergrad Igma notation 2i-1 = 2n, for all n is an element of N

    prove or disprove n sigma notation 2i-1 = 2n, for all n is an element of N. i=1 N = natural numbers
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    Graduate Using the definition of the binary product

    Prove or find counterexamples: If A x B = empty set then A = empty set or B = empty set.
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    Undergrad Prove or find counterexamples

    Yes, they're equal. It's called the Associative Property of Multiplication. The property which states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping: (a . b) . c = a . (b . c)
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    Undergrad Prove or find counterexamples

    ..using only the definition of the binary product: for any sets A, B, C in a universe U: (A x B) x C = A x (B x C) I have no clue how to even get started with this one. Somebody help me please!
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    Graduate Set Theory Theorems: Solving for A in A ∩ B = C ∩ B and A ∩ B' = C ∩ B

    I understand the example you mentioned above but i still don't get this: A = (AnB) U (AnB') = (CnB) U (CnB') = C i don't get how you figure that out! still doesn't make sense to me
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    Prove/Find Counterexample: Intro to Set Theory

    alright. thank you so much!
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    Therefore, B is not a subset of UProving A n B = U iff A = U and B = U

    thanks! it really helps!
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    Prove/Find Counterexample: Intro to Set Theory

    Homework Statement Prove or find counterexamples. For any sets A, B, C in a universe U: if A union C contained B union C then A contained B Homework Equations none. The Attempt at a Solution im just not sure if i did it right. id appreciate if you can check my work and let me...
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    Therefore, B is not a subset of UProving A n B = U iff A = U and B = U

    Homework Statement Prove the following: For any sets A, B, C in a universe U: A n B = Universe iff A = Universe and B = Universe Homework Equations none. The Attempt at a Solution I tried to do the questions but I am just not sure if i did it right. id appreciate if you can...
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    Is A Contained in B Equivalent to A Intersecting B Equals A?

    Homework Statement Prove A contained B iff A n B = A Homework Equations none The Attempt at a Solution I tried to do the questions but I am just not sure if i did it right. id appreciate if you can check my work and let me know what changes i have to make. thanks the symbol...
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    Graduate Set Theory Theorems: Solving for A in A ∩ B = C ∩ B and A ∩ B' = C ∩ B

    Thank you but i'm a little bit confused now.. Let me just translate what you wrote, So, A = A*B + A*B' = C*B + C*B' = C becomes A = (AnB) U (AnB') = (CnB) U (CnB') = C the symbol "n" for intersect A = AnB U AnB' results from 2 things, distributive law for sets [An(BUB') = AnB...
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    How Do You Prove Set Theory Relations and Operations?

    -------------------------------------------------------------------------------- I tried to do the questions but I am just not sure if i did it right. id appreciate if you can check my work and let me know what changes i have to make. thanks the symbol "n" means "intersect" U for Union...