Please write nice a clear on a paper.
Please write nice a clear on a paper. 2. For sets A, B, and C, prove (A-B) _ (B _ C) = A-B LS R: 2. For sets A, B,...
Write a clear line, please explain the steps let R. is aring and R. is a ring 2 show that R. @ R is a ring ring? Z prove
SHOW STEPS ON A PAPER WITH A CLEAR HANDWRITING PLEASE.
a) If the sets Xand Yare non-mutually exclusive, show hat: b) Given two events X and Y, draw a Venn diagram to demonstrate that P(X) P(XnY)+ P(X nY), and deduce that P(X)- P(X/Y)P(Y) + P(X/Y)P(Y)
PLEASE answer it nice and clear to be read
2. Find the Z-Inverse for the following fractions, [40 points] z(2z-1) (b) X2(z) =FT(HS) (z-2) (z-3)
2, For each of these sets. A={3n : n E N), B = {r E R : x2 < 7), and C = {x E R : x < 12), (i) Is the set bounded above? Prove your answer.] ( .] ii) Is the set bounded below? Prove your answer answer the following questions:
Let A, B and C be sets. Prove
Please be clear.
2. Prove that the columns of a matrix A are linearly independent if and only if Ax = 0 has only the trivial solution. 3. Prove that any set of p vectors in R™ is linearly dependent if p > n.
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.
Let A,B and C sets. Assume A ⊂ B ⊂ C, prove C \B = C \(A∪B)
Let A, B, and C be sets. Prove the following statement: (A − B) ∩ (C − A) = ∅
Please, I need clear writing if you choose to write by hand for
a,b,c, and d.
thanks,
5. In each step, explain clearly what property or axiom you are using. (a) Prove "inclusion-exclusion," that PAU B)-P(A)+P(B)-Pan B) (b) Prove the "union bound" that P(Ai UA2) P(Ai) P(A2). Under what conditions does the equality hold? (c) Prove that, for A and A2 disjoint, P(A UA2 B) P(A B)P(A2 B) (d) A and B are independent events with nonzero probability. Prove whether...