Prove or give a counterexample to each of the following statements: (a) If A and B2 are independent then P(A|B1 ∩ B2) = P(A|B1) (where P(B1 ∩ B2) > 0).

Q: 2 Let A= then det(3A") = 6- -2 - 18 -6

A:

Q: Let n EU = Z and p(n): n² + n is an even integer. a. Write the following statement: (Vn) p(n). b. Is…

A: (a) Here, the given statement is: For ∀n∈U=ℤ, p(n):n2+n is an even integer.

Q: X7. We know that given any real numbers x1 and x2, if x1x2 = 0, then x1 = 0 or x2 = 0. Since there…

A: (b) given any real number x1 , x2 , x3 , x4 claim- if x1x2x3x4=0 then x1=0 , x2=0 , x3=0 , x4=0

Q: Q7. Show that 2F₁ (1,2; 1; -x) = In(1+x) x

A: Step 1:Step 2:Step 3:Step 4:

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: The following is a valid identity, true or false? P(k): 1+2+22 +23 + .. +2k = (2(k+1)/2) +…

A:

Q: snip

A: Given: A=2131-10 and B=102132   (a) To find: AB

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

A:

Q: 17 3. Evaluate: de (r- 1)(2 + 16)

A:

Q: Evaluate the following commutators [Â, B] = ÂB – BÂ. Hint: use an arbitrary function that cancels at…

A: a x,PxPx=-ih∂∂xx,Pxφ=x,-ih∂∂xφ=-ihx∂φ∂x+ih∂∂xxφ=-ihx∂φ∂x+ih∂φ∂x+ihφ=ihφ∴x,Px=ih

Q: 2. |a + ib|= √a² + b² O True O false

A: This question is based on modulus of complex number.

Q: Prove that A2=I.

A:

Q: Let (4A)−¹= 2 4 -3 2 Get At.

A:

Q: If A and B are mutually exclusive, then _____. a P(A) + P(B) = 0 b P(A) + P(B) = 1 c P(A I B) = 0 d…

A: here given data that  If A and B are mutually exclusive, then __we have to find out the correct…

Q: Compute |A| for the following:

A: We have to compute A for the following given matrix: A=210121012 We know to determine the…

Q: 2. Show that for all positive real numbers a and b, if a < b then a² < b².

A:

Q: Find the string that has this generating function: a) (1− x)−3 b) (1+2x)−4 c) 1/(1 −3x)3

A:

Q: (b) Given integers a, b and c such that cla and cb then c|(ar + bs) for all r, s E Z. True False &…

A: Given that c|a and c|b for some given integers a,b and c The statement is c|ar+bs for all r,s∈ℤ…

Q: b.) 3x-2y < 12

A:

Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

A:

Q: If, (V₁ X V₂) · V3 = 6.5 then what is (V3 X V₁) - V₂? ○ (0,0,0) Cannot be found with the given…

A:

Q: (d) The third quartile for X 提交答案| Tries 0/5 (e) the IQR for X 提交答案| Tries 0/5 (f) P(IX-216|> 41)

A: Given : Let X be a r.v X~N(216 , 18) Here ; μ=216 σ=18

Q: Suppose SCR is a set of numbers. (a) Define inf(S) and sup(S). (b) Show that inf(S) = - sup(-S). (c)…

A: Set: A well-defined collection of objects or numbers is called a set. We can write a set in two…

Q: 1. Prove that (fn+1fn+3 – fnfn+4)* = 4 for each positive integer n.

A: We need to prove this, fn+1fn+3-fnfn+42=4

Q: -1 -2 -3 -4- 1 2 Let A = 1 1-

A:

Q: Find the term of (a – 2b)3 that has b in it. |

A:

Q: B Given that p(A| B)=0, and p(A)=.15, are A and B (a) independent? (b) exclusive?

A: Ans#- Given, P(A | B) = 0, and P(A) = 0.15.            Are A and B        (a) Independent?…

Q: If xER then |1– x| = |x+1|- True O False

A: We have check given statement is true or not

Q: onditions, if any, must be set forth in order for a + b to be equal to n(A U B)?

A: In this question, the concept of Set Operations is applied. Set Operations The concept of set…

Q: В Calculate A and B so that + %D 1+x 1-

A: