Math 290 Questions and with detailed accurate solutions and with a grade of A+

Commutative Laws - ANS(1) A U B = B U A (2) A ∩ B = B ∩ A Associative Laws - ANS(1) A U (B U C) = (A U B) U C (2) A ∩ (B ∩ C) = (A ∩ B) ∩ C Distributive Laws - ANS(1) A U (B ∩ C) = (A U B) ∩ (C U A) (2) A ∩ (B U C) = (A ∩ B) U (C ∩ A) De Morgan's Laws - ANS(1) A U B (line over whole thing) = A ∩ B (lines over individual letters) (2) A ∩ B (line over whole thing) = A U B (lines over individual letters) Start a direct proof (P implies Q) - ANSassume P is true show Q is true Start a contrapositive proof (P implies Q) - ANSassume Q is false show P is false Start a contradiction proof (P implies Q) - ANS(1) assume P is true and Q is false find a contradiction (2) assume (P implies Q) is false find a contradiction surjective function ƒ: A → B - ANS***ONTO (V z∈B)(∃ x∈A)(g(x)=z) injective function : A → B - ANS***ONE-TO-ONE (V x₁,x₂∈A)(x₁≠x₂ = f(x₁)≠f(x₂)) or (V x₁,x₂∈A)(f(x₁)=f(x₂) = x₁=x₂) N - ANSNatural Numbers {1,2,3,...} Z - ANSIntegers {...,-2,-1,0,1,2,...}