Carefully go through the steps of the proof below. Then answer the questions at the end. Claim. AC A, for any set A. Pro

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Carefully Go Through The Steps Of The Proof Below Then Answer The Questions At The End Claim Ac A For Any Set A Pro 1 (147.76 KiB) Viewed 35 times

Carefully go through the steps of the proof below. Then answer the questions at the end. Claim. AC A, for any set A. Proof. (1) U is a set (2) (3) 9 U arbitrary ‘u € U' is false or ‘u € U’ is true uɛU ⇒ u EU 9 u arbitrary ; by ; by ; by (4) Vx [x EU →⇒ x €U] (5) UCU (6) U is a set ⇒ U CU (7) VX[X is a set ⇒ X CX] (1) Decide whether this is: (i) direct proof – (ii) proof by contraposition – (iii) proof by contradiction - (iv) proof by cases. ; by ; by ; by ; by (2) Decide whether the proof is correct or not. (2a) If the proof is incorrect, identify the first line where a mistake happens. (26) If the proof is correct, fill in the blanks by choosing from the following list: (i) by algebra – (ii) by assumption – (iii) by closure – (iv) by definition – (v) by definition, for some suitable choice of k (when you enter your answers on Brightspace, you may use the abbreviated form in boldface) – (vi) by logic. [2P]