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303a1solns - ASSIGNMENT 1 SOLUTIONS MATH 303 FALL 2011 If...

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ASSIGNMENT 1 – SOLUTIONS MATH 303, FALL 2011 If you find any typos or other errors please let me know. Manipulation (M1) {{{∅} , {∅}} , {∅ , {∅}} , {{∅}}} = {{{∅}} , {∅ , {∅}} , {{∅}}} = {{{∅}} , {∅ , {∅}}} (M2) There are a number of possible approaches, here is one way Assume A B . We want to show A B = B . It is always the case that B A B , so if we can show A B B then we will be done. Lets try to do that. Take any element x A B . Then we know that x A or x B . In the first case we have x A B , and so x B . Thus either way x B , and so A B B which is what we needed to show. (M3) There are a number of possible approaches, here is one way Supposse A B = B . Take any x A . Then x A B , so x B . Thus A B . (M4) S C = {∅} ∪ {∅ , {∅}} ∪ ∅ = {∅ , {∅}} . (M5) (1 point) To start we have . Pair with to get {∅ , ∅} = {∅} . Pair {∅} with itself to get {{∅}} . Pair {∅} with to get {∅ , {∅}} .
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