Recent content by rallycar18

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    Is x Equivalent to y in Congruence Class Equivalence?

    Homework Statement "Prove that if x is an element of [y] then [x] = [y]"
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    Proving Equivalence Classes in Modular Arithmetic

    Homework Statement Suppose [d], [b] \in Z sub n.
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    Proving Injectivity: f ∘ g = f ∘ h ⇒ g = h

    Then f^(-1) : Y → X is also injective.. but I don't see what I can do from that.
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    Proving Injectivity: f ∘ g = f ∘ h ⇒ g = h

    Definition of injective for If f : X → Y : For all y \in Y, there exists at most one x \in X such that f(x) = y Because f : X → Y and g, h : W → X, f ∘ g : W → X → Y and f ∘ h : W → X → Y so f ∘ g, f ∘ h : W → Y that's where I get stuck.
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    Proving Injectivity: f ∘ g = f ∘ h ⇒ g = h

    Prove that: If f : X → Y is injective, g, h : W → X, and f ∘ g = f ∘ h, then g = h.
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    Group theory, subgroup question

    Thanks, mark- i left that out. A subset A of a group (G,*) is called a subgroup if the elements of A form a group under *. * is the binary operation of the two groups.
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    Group theory, subgroup question

    Let A be a subgroup of G. If g \in G, prove that the set {g^{-1} ag ; a \in A} is also a subgroup of G. Thanks for any help.
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    Proving Set Theory Union in Cartesian Products

    I'm not familiar..
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    Proving Set Theory Union in Cartesian Products

    Homework Statement Suppose A,B,C are sets. Prove that A× (B U C)= (AxB) U (C x A)