Venn diagram

1. (a) Compute gcd(132,84). (b) Suppose a,b ∈N are co-prime. What is gcd(a,a + b)? 2. For sets A and B, define A∗B to be (A∪B)c (the complement of A∪B). (a) Simplify (A∗B)∗(A∗B). Justify your answer (e.g. using a Venn diagram or some other technique). (b) Express Ac using A and ∗. Justify your answer. (c) Express A∩B using A, B, and ∗. Justify your answer. 3. (a) List all possible functions f : {a,b,c}→{0,1} (b) Describe a connection between your answer for (a) and Pow({a,b,c}). (c) In general, if card(A) = m and card(B) 1. (a) Compute gcd(132,84). (b) Suppose a,b ∈N are co-prime. What is gcd(a,a + b)? 2. For sets A and B, define A∗B to be (A∪B)c (the complement of A∪B). (a) Simplify (A∗B)∗(A∗B). Justify your answer (e.g. using a Venn diagram or some other technique). (b) Express Ac using A and ∗. Justify your answer. (c) Express A∩B using A, B, and ∗. Justify your answer. 3. (a) List all possible functions f : {a,b,c}→{0,1} (b) Describe a connection between your answer for (a) and Pow({a,b,c}). (c) In general, if card(A) = m and card(B)

 
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