Define with normS (n) (22) | I(M) WK.P() ⑥HK (~) H' (~~) and H) 2² (^_^)

Draw the Venn diagram with the following information: ANBNC={√2, √-1}, (ANB)NC'={2%⁰, ∞0}, (ANC)NB'={N, Xo}, (BNC)NA'={T, 1010⁰0}, A-(BUC)={~, €, ≤}, B-(AUC)={Z, Ø}, C—(AUB)={ (1+ √5)/2, Q}, and (AUBUC)'={R, 0, 1}

2. Let B = [ 4 ] - ^ - [ 4 ] - - - - { { } } } [{ } ] }- (a) in span(B)? Justify your answer. (b) Is V2 Is v₁ in span(B)? Justify your answer.

Let f and g be any permutations. Show that the order of h=fgf^(-1) is the same as the order of g.

Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2 are independent, then X2~ X-,

Let à = ст -5' -4 Find ||a, the norm of a.

Find projs u. 2 span{ [ _² ] [ 8 ] }; " = [-²] u -1 1 S = span projs u = 00

Prove S^2 is simply connected.

10) Find / 2(3z* +1)² dæ

Prove ¬¬A := ¬(¬A) = A ¬(A ^ B) = (¬A) V (¬B) ¬(A V B) = (¬A) ^ (¬B) (Vx € X: E(x)) = (x € X : ¬E(x))