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- Show that the following statement is false. If A and B are two sets of positive integers, then (A∪B)^'=A'∪B'. Include the following in your answer: What technique seems appropriate in this situation? Why? Prove this statement true. Explain the elements of all sets that you use in your answer.26 of 40 Consider the Datalog programs P1 (left) and P2 (right) below, which use relations R(A, B) and S(A, B). P1 P2: T1(A) R(A, B). T4(A) R(A, B), S(A, B). T2(A) S(A, B). T3(A) + T1(A), T2(A). Which of the following statements is TRUE about the relationships between relations T3 and T4 defined by P1 and P2, respectively? Note that the commas "," used in the rule bodies to separate the predicates is the same as using AND. Select one: T3 and T4 include the same set of tuples. Every tuple in T3 is also contained in T4, that is, T3 C T4. O None of the other answers, that is, T3 and T4 contain different tuples, in general. O Every tuple in T4 is also contained in T3, that is, T4 C T3.Let A = {1,2} and B = {3, 4}. (a) Find A x B (b) How many subsets Ax B of size 2 are there? List all the possible subsets
- If U1 and U2 are both upper triangularmatrices, and L1 and L2 are lower triangular which of the following are triangular? [U1+U2, U1U2, U2^2, U1+L1, U1L1, L1+L2].(4) Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C) = (A × B) \ (A × C). Prove that (A x B) n (C x D) = (ANC) × (BND).Each time a component is tested, the trial is a success (S) or failure (F). Suppose the component is tested repeatedly until a success occurs on three consecutive trials. Let Y denote the number of trials necessary to achieve this. List all outcomes corresponding to the five smallest possible values of Y. (Enter your answers in set notation.) what is the answer for Y=7. I have {SFFFSSS,SSFFSSS,FFFFSSS,FSSFSSS,FSFFSSS. Are there more?