1. Z

    Bezout's Identity converse

    Bezout's Identity: If d = gcd(m,n), there exist integers A and B st d=Am+Bn. (proved by Euclid's algorithm} 1) Is there a converse? 2) How would you express it? 3) How would you prove it?
  2. T

    Stating the converse, converse of if x=y then x^2 = y^2?

    If x = y, then x^2 = y^2 I am asked to state the converse. Ive been told in the book to flick the If and then around so I done that but the converse of this theorem is If x^2 = y^2 then x \neq y from the answer in the book. How does that work? Why If x^2 = y^2 then x = y is not the...
  3. T

    Circle theorems and their converse

    I kind of don't understand what the converse of these three theorems are: 1. The angle in a semi-circle is a right angle. 2. The perpendicular from the centre of a circle to a chord bisects the chord. 3. The tangent to a circle at a point is perpendicular to the radius through that point...
  4. R

    Is there a statement equivalent to its own converse?

    I know of a lot of pairs or sets of mathematical statements that are equivalent to each other, e.g.: Pasch's axiom and the plane separation axiom, the different statements of the axiom of choice, Playfair's axiom and Euclid's fifth postulate. That got me wondering, is there any mathematical...
  5. O

    Help on converse proof for function extensionality

    Hi there, I am going through the book abstract algebra by Deskins. In one of the excercises (Ex 1.3, No. 9 ), the question is on proving the converse of the following theorem: if F and G are functions, if {domain of F} = {domain of G} = S, and if sF = sG for every s \in S,then F = G. We need to...
  6. J

    Statements: Converse, Contrapositive and Negation

    Let S be the following statement: For all function f, if f is differentiable at a, then f is continuous at a. (i) Write the converse of the statement of S (ii) Write the contrapositive of the statement of S. (iii) Write the negation of the statement of S.
  7. O

    Set theory. Is the converse true?

    1. The problem statement, all variables and given/known data Prove that \cup_{x \in C} \{ 2^{x} \} \subseteq 2^{\cup C} 2. Relevant equations \cup_{x \in C} \{ 2^{x} \} = \{ A | \exists x \in C, A \subseteq 2^{x} \} 2^{x} is the powerset of x. i.e. 2^{x} = \{ y | y \subseteq x \} 3. The...
  8. S

    Prove converse of Addition Princciple

    I feel like I'm getting better at proofs. But I'm not convinced this one is good enough. Can someone "grade" this for me? Note that this is in the chapter on contradictions, so I shouldn't really use a direct proof. Thanks Prove: For finite sets \left| A \cup B \right| = \left| A \right| +...
  9. S

    Counterexamples to the converse of Lagrange's theorem

    The most famous counterexample that tells us the converse of Lagrange's theorem in general does not hold is A_4; 6 divides its order but it does not have any subgroup of order six. But what are the other interesting counterexamples?
  10. R

    converse,inverse,contrapositive. My brain is fried help!

    If I live in Atlantic City, then I live in New Jersey. Please, give: (a) the converse (b) the inverse (c) the contrapositive