2. Suppose A,B,C,D are sets. We know that (A x B)U(C x D) S (AUC) x (BUD). (a) Give an example where the inclusion is strict (i.e. the sets in LHS and RHS of the inclusion above are not equal). (b) Make a conjecture under which assumptions on A,B,C, and D the sets in RHS and LHS are in fact equal.
Prove equalities involving sets A, B, C and D a) (AIB)U(C1B) = (AUC) IB b) (AUB)-(ANB) = (A-8)U(-A) c) (AxB) OLC xD) - (ANC) x (BND) d) (AXB) (BAA) = (ANB)X(AMB)
10. Let A, B, and C be sets. (a) Prove or disprove: if A - C CB-C, then ACB. (b) State the converse of part (a) and prove or disprove.
61. Prove or sets A, B, and C disprove: A A (BnC) (A A B) n (A A C) for all
Use Venn diagrams to prove or disprove the following c) AU B (An B) u (A n B)u (A n B) d) A U (B n C) (AU B) n (AU C)
discrete math question using proofs to determine to prove the following equation or disprove it 4. Prove or disprove. Let A, B, C, and D be sets. Then (Ax B)n (CxD) (Ancx (B nD) 5. Prove or disprove: {2k 1 k E Q} {4" | k E Q) F6 7 Prove or disprove. Let A be a set and let I be an arbitrary index set for a collection of sets {Be l α E 1). Then, 6. An(UP)-a αΕΙ
Consider the utility function u(x) = ax + b e^cx where a, b, c are positive scalars. (a) Compute the coefficient of absolute risk aversion. (b) Describe the risk attitude represented by u(x) and how it changes as x increases. (c) Write down the equations to determine the certainty equivalent and the risk premium of a gamble X for an individual with initial wealth w > 0. (d) What is the sign of the risk premium? How does the risk...
4. Prove for all ne Zt and all sets A1, A2,..., An, B that (Ax – B) = that ---- () --
Please help answer all parts! (1) Prove that 75 is irrational. (State the Lemma that you will need in the proof. You do not need to prove the lemma.) (2) Disprove: The product of any rational number and any irrational number is irrational. (3) Fix the following statement so that it is true and prove it: The product of any rational number and any irrational number is irrational. (4) Prove that there is not a smallest real number greater than...
6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A) 6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A)