Recent content by fatineouahbi

Hello Euge , I never would've thought of that ,thank you so much for your help !

Let f be an application from E to E (E≠∅) such that f∘f∘f = f Prove f is an injection ⇔ f is a surjection I honestly have no idea how to start and I'd love to know the answer before my math exam tomorrow morning (Thinking)

1.Prove f(A⋂B) ⊂ f(A) ⋂ f(B) 2.Prove f(A) ⋂ f(B) ⊂ f(A⋂B) ⟺ f is an injection I've solved the first question , as for the second I started with f(A) ⋂ f(B) ⊂ f(A⋂B) ⇒ f is an injection this way : Let's suppose f(a) = f(b) = p If we consider A = {a} and B = {b} then f(A) = f(B) = p then f(A) ⋂...

Okay,thanks a lot !

Thank you !

Let A,B and C be three elements of P(E) 1. Solve in P(E) the following equation : AUX=B 2. Let's suppose that C ⊂ A ⊂ B , solve in P(E) the following system : AUX=B and A⋂X=C I've already answered the first question , it's X = (B\A) U Y such that Y∈P(A) As for the second , I thought maybe X=C...

Let A,B,C be three sets such that : A={x∈ ℤ / x=11k+8 , k∈ℤ} B={x∈ ℤ / x=4k , k∈ℤ} C={x∈ ℤ / x=11(4k+1) -3 , k∈ℤ } Prove A⋂B = C I started with this : Let x be an arbitrary element of A⋂B then ∃(k,k')∈ ℤ² such that x=11k+8 and x=4k' then 11k+8 = 4k' then 11(k+1)-3 = 4k' I don't know where...

Thank you so much !

Hello :) Thank you , I think I may get it now ? (x ∈ A and y ∈ B\C) or (x ∈ A and y ∈ C\B) then p ∈ Ax(B\C) or p ∈ Ax(C\B) then p ∈ (AxB) \ (AxC) or p ∈ (AxC) \ (AxB) thus p ∈ (AxB) △ (AxC) then Ax(BΔC) ‎⊂ (AxB) Δ (AxC) Then I'll just try to go backwards maybe ?

Let A,B,C be three sets . Prove Ax(BΔC)= (AxB) Δ (AxC) I tried to start with this : Let p be an arbitrary element of Ax(BΔC) then p=(x,y) such that x ∈ A and y ∈ (BΔC) x ∈ A and (y∈ B\C or y∈ C\B) (x ∈ A and y ∈ B\C) or (x ∈ A and y ∈ C\B) But I don't know how to continue or if I should even...