Wikipedia
math set theory logic : Set theory is the branch of mathematics that studies sets, .... CZF, and IZF, embed their set axioms in intuitionistic logic instead of first order logic. ..... More from Wikipedia
Sets Introduction
Introduction - In Mathematics, a well-defined collection of definite objects is called a set. George Cantor is regarded as the "Father of Set theory". The concept of "Sets" is basic in all branches of mathematics. It has proved to be of pa..
Introduction
In Mathematics, a well-defined collection of definite objects is called a set. George Cantor is regarded as the "Father of Set theory". The concept of "Sets" is basic in all branches of mathematics. It has proved to be of particular import..
In this first clip on the mathematical foundations of probability, I describe logical propositions and set theory. The concepts introduced will be realtively easy (hopefully), and may not be strictly necessary for the rest of the series. Still for a full understanding of the core mathematics, the clip is recommended. Check out video #4 for a graphical representation of the ideas in this series. For those who find graphics easier than algebraic expressions, it may be illuminating: www.youtube.com...
Algebra tutoring for finite math includes discussing the subjects of set theory, logic and probability. Learn finite math subjects like statistics and geometry with assistance from amath teacher in this free video on mathematics. Expert: Jimmy Chang Contact: www.wearehdtv.com Bio: Jimmy Chang has been a math teacher at St. Pete College for more than nine years. He has a master's degree in math and his specialties include calculus, algebra, liberal arts math, and trigonometry. Filmmaker ...
Question : A survey of 300 Parks showed the following:
15 had only camping
20 had only hiking trails
35 had only picnicking
185 had camping
140 had camping and hiking trails
125 had camping and picnicking
210 had hiking trails
Find the number of parks that:
a. Had at least one of these features?
b.Had all 3 features?
c.Did not have any of these features?
d.Had exactly two of these features?
Answer : It is easy if you can draw a graph and plot the stuffs Let A represent camping B represent hiking trails C represent picnincking U represent universal set a - only camping b - only hiking trails c - picnicking x - both camping and hiking trails alone y - both hiking trails and picknicking alone z - both camping and picknicking alone r - all the three so putting the variables a = 15 b = 20 c = 35 x + r = 140 z + r = 125 a + x + r + z = 185 ==> a + z = 185 - 140 = 45 z = 30 c + y + r + z = 210 ==> 35 + y + 125 = 210 y = 50 also z + r = 125 so r is 95 and hence x is 45 (x + r = 140) so finally all the values are fetched a, b, c is 15,20, 35 x,y,z is 45,50,30 r is 95 so had at least one feature is sum of a+b+c+x+y+z+r which is 290 had all three features is r which is 95 had exactly two features is sum of x,y,z which is 125 so adding all its 290 so among total of 300, 10 people didn't have any features so final answers 290 95.... More from Yahoo Answers
Answer : It is easy if you can draw a graph and plot the stuffs Let A represent camping B represent hiking trails C represent picnincking U represent universal set a - only camping b - only hiking trails c - picnicking x - both camping and hiking trails alone y - both hiking trails and picknicking alone z - both camping and picknicking alone r - all the three so putting the variables a = 15 b = 20 c = 35 x + r = 140 z + r = 125 a + x + r + z = 185 ==> a + z = 185 - 140 = 45 z = 30 c + y + r + z = 210 ==> 35 + y + 125 = 210 y = 50 also z + r = 125 so r is 95 and hence x is 45 (x + r = 140) so finally all the values are fetched a, b, c is 15,20, 35 x,y,z is 45,50,30 r is 95 so had at least one feature is sum of a+b+c+x+y+z+r which is 290 had all three features is r which is 95 had exactly two features is sum of x,y,z which is 125 so adding all its 290 so among total of 300, 10 people didn't have any features so final answers 290 95.... More from Yahoo Answers
Question : Prove or Disprove:
a) If R is an equivalence relation on a nonemtpy set A, then R can be irreflexive.
b) Let A be a set. If A B = Empty Set for every set B, then A = Empty Set.
c) There exists a smallest positive real number.
d) Let A, B, C be sets. If A U B = A U C, then B = C.
help with proving or disproving please... Mo....for part d) doesn't the assumption have to be A U B = A U C ? for the sets u gave me...that doesnt equal each other...
Answer : (a) Use the definition of a equivalence relation (if I'm right, it by definition is reflexive) (b) A B = null for every set B Then let B=A (c) Assume there is a smallest positive real, then take half of it. (d) It's false. Let A = {1, 2}, B = {1} and C = {2} for a (somewhat) nontrivial counterexample. -Edit for Asker/Voters- In my example: A U B = {1, 2} U {1} = {1, 2} A U C = {1, 2} U {2} = {1, 2} Therefore A U B = A U C. However {1} is not equal to {2}... More from Yahoo Answers
Answer : (a) Use the definition of a equivalence relation (if I'm right, it by definition is reflexive) (b) A B = null for every set B Then let B=A (c) Assume there is a smallest positive real, then take half of it. (d) It's false. Let A = {1, 2}, B = {1} and C = {2} for a (somewhat) nontrivial counterexample. -Edit for Asker/Voters- In my example: A U B = {1, 2} U {1} = {1, 2} A U C = {1, 2} U {2} = {1, 2} Therefore A U B = A U C. However {1} is not equal to {2}... More from Yahoo Answers
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