Question 1 (2 points) Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Find the set corresponding to the bit string 1000000001. Avoid using any spaces in your answer. 5/ Question 24 0 l 2 points Below is given a proof of a result. Proof: Assume thatx is even. Then x = 23 for some integer 3. So 3:32 4:1:5=3(2a,)2 4(2a) 5= 12a,2 8a5 =2(6a.2 4a3)l1. Since 60.2 4a 3 is an integer, 32:2 4a: 5 is odd. Determine which of the following statement(s) were proven by the above proof. If 31:2 4m 5 is even, then x is even. If 33.-2 4m 5 is odd, thenx is odd. If x is even, then 33:2 4m 5 is odd. If x is odd, then 31:2 4m 5 is even. If x is even, then 3:132 4m 5 is even. If 33:2 4m 5 is even, then x is odd. lfx is odd, then 3:1:2 4:1: 5 is odd. If 31:2 4m 5 is odd, then x is even. Question 3 (2 points) Below is given a promc of a result. Proof: Assume that x is odd. Then x = 2b+1 for some integer b. 50 33:2 4m5 = 3(2b+1)2 4(2b+1)5 = 3(4b2+4b+1 Sinceb2 + 2b 3 is an integer, 3382 4.7: 5 is even. Determine which of the following statement(s) were proven by the above proof. ._. lfx is odd, then 3:1:2 4:1: 5 is odd. ._.. lfx is even,then 31:2 43!: 5 is odd. ._. If 3:132 4:13 5 is even, then x is odd. .._.. lfx is even,then 335:2 43!: 5 is even. .i. If 3:132 4:13 5 is even, then x is even. ._.. If 33:2 4a: 5 is odd, then x is odd. .i. If x is odd, then 3132 4:1! 5 is even. .._. If 31:2 4:13 5 is odd, then x is even. \fQuestion 8 (2 points) Fuzzy sets are used in artificial intelligence. Each element in the universal set U has a degree of membership, which is a real number between 0 and 1 (including 0 and 1), in a fuzzy set S. The fuzzy set S is denoted by listing the elements with their degrees of membership (elements with 0 degree of membership are not listed). For instance, we write {0.6 Alice, 0.9 Brian, 0.4 Fred, 0.1 Oscar, 0.5 Rita} for the set F (of famous people) to indicate that Alice has a 0.6 degree of membership in F, Brian has a 0.9 degree of membership in F, Fred has a 0.4 degree of membership in F, Oscar has a 0.1 degree of membership in F, and Rita has a 0.5 degree of membership in F (so that Brian is the most famous and Oscar is the least famous of these people). Also suppose that R is the set of rich people with R = 10.4 Alice, 0.8 Brian, 0.2 Fred, 0.9 Oscar, 0.7 Rita}. The union of two fuzzy sets S and T is the fuzzy set S U Z, where the degree of membership of an element in S UT is the maximum of the degrees of this element in S and in T. Which of the following fuzzy sets represent FUR. ( 10.2 Alice, 0.1 Brian, 0.2 Fred, 0.8 Oscar, 0.2 Rita} 10.5 Alice, 0.85 Brian, 0.3 Fred, 0.5 Oscar, 0.6 Rita} 10.6 Alice, 0.9 Brian, 0.4 Fred, 0.9 Oscar, 0.7 Rita} 10.4 Alice, 0.8 Brian, 0.2 Fred, 0.1 Oscar, 0.5 Rita} {Alice, Brian, Fred, Oscar, Rita} Of1 Alice, 1.7 Brian, 0.6 Fred, 1 Oscar, 1.2 Rita} ONone of the other choicesQuestion 9 (2 points) Fuzzy sets are used in artificial intelligence. Each element in the universal set U has a degree of membership, which is a real number between 0 and 1 (including 0 and 1), in a fuzzy set S. The fuzzy set S is denoted by listing the elements with their degrees of membership (elements with 0 degree of membership are not listed). For instance, we write {0.6 Alice, 0.9 Brian, 0.4 Fred, 0.1 Oscar, 0.5 Rita} for the set F (of famous people) to indicate that Alice has a 0.6 degree of membership in F, Brian has a 0.9 degree of membership in F, Fred has a 0.4 degree of membership in F, Oscar has a 0.1 degree of membership in F, and Rita has a 0.5 degree of membership in F (so that Brian is the most famous and Oscar is the least famous of these people). Also suppose that R is the set of rich people with R = 10.4 Alice, 0.8 Brian, 0.2 Fred, 0.9 Oscar, 0.7 Rita}. The intersection of two fuzzy sets S and T is the fuzzy set S n T, where the degree of membership of an element in S n T' is the minimum of the degrees of this element in S and in T. Which of the following fuzzy sets represent Fn R. Of1 Alice, 1.7 Brian, 0.6 Fred, 1 Oscar, 1.2 Rita} 10.6 Alice, 0.9 Brian, 0.4 Fred, 0.9 Oscar, 0.7 Rita} 10.2 Alice, 0.1 Brian, 0.2 Fred, 0.8 Oscar, 0.2 Rita} None of the other choices 10.5 Alice, 0.85 Brian, 0.3 Fred, 0.5 Oscar, 0.6 Rita} 10.4 Alice, 0.8 Brian, 0.2 Fred, 0.1 Oscar, 0.5 Rita} {Alice, Brian, Fred, Oscar, Rita}Question 11 (2 points) When attempting to prove the statement "If n is an integer such that 3n+2 is even, then n is even." by contraposition, determine which of the following options describes such an approach. We assume that n is an integer such that n is even, and we attempt to show that 3n+2 is even by using axioms, definitions, previously proven theorems, and rules of inference. Q We assume that n is an integer such that 3n+2 is even and n is even, and we attempt to find a contradiction by using axioms, definitions, previously proven theorems, and rules of inference. "j, We assume that n is an integer such that 3n+2 is odd and n is odd, and we attempt to find a contradiction by using axioms, definitions, previously proven theorems, and rules of inference. c: None of the other choices We assume that n is an integer such that 3n+2 is odd, and we attempt to show I that n is odd by using axioms, definitions, previously proven theorems, and rules of inference. We assume that n is an integer such that n is odd, and we attempt to show that 3n+2 is odd by using axioms, definitions, previously proven theorems, and rules of inference