Show that if a|b then -a|b.

Q: _If A = Verify that [A-!]" = [A"]¬1 ? l1 2.

A:

Q: a – b -| < 1, if|a| < 1, and |b| < 1. 1- āb - Show that|-

A: From the given information. For , then show that .

Q: Prove that (AXB)×C=B(A • C)-C(A • B).

A: The solution is given in the next step.

Q: 3. Prove that (An B)² C A × B.

A:

Q: Let 21 = 2+ j3 and z 4 j5. Evaluate

A:

Q: b) Show that XNOT =

A:

Q: An element x is in A ∪ B if, and only if, _____________________.

A: Known fact: A∪B=x | x∈A or x∈B

Q: Prove: If a &gt; 0, then (1/a) &gt; 0.

A: It is given that a&gt; 0.It is known that if ab &gt; 0 then a &gt; 0 or b &gt; 0 or a&lt; 0 or b…

Q: Let X-Bin(5,0.5), then P(x >3|x >2) is

A:

Q: Let ā = and b . Find 3ā + b. -

A: We will simply use vector addition rules to find the answer

Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: Let, a, = 3, a2 = 4 and for n2 3, a,= 2an-1+ an-2 + n + 1, express a, in terms of n. %3D %3D %3D

A: The nth term of A.P is given by an=a+n-1d we have,  a=3,d=4-3=1an=3+n-11=2+n we get,…

Q: HeW. By the Same way Prove that: X Ju (x) (X)

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Q: so-Z of what is 21

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Q: Show that 1-r for any r 1 1 and any 3. nEN

A: answer

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: If A=A ˆ ,then A must equal to either I or -I. Select one: O True O False

A: As you post multiple question according to guideline I only stop the first one please post other…

Q: If x=y+qp and f=xy+qp² Express x in terms of q,p and f

A:

Q: 4. Let b > a > 0. Show that (a,b] is neither closed nor open.

A: Explanation of the solution is given below....

Q: Show that 1 – R1.23 = (1 – r12²) (1 – r13,22 ) Deduce that (i) R, 23 2r,2, (ii) R? = r12² + r13², if…

A: Answer: For the given data,

Q: Find a and b such that 2 1 = a -4 + b -4

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Q: b22 Such that/2/-1E andArg 4.

A: We find complex number

Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: Exercise 6 If az, a2, .,a, and by, b2, ..., b, are two sets of positive numbers arranged in…

A:

Q: Prove by contraposition that if x^5 + 7x^3 + 5x >= x^4 + x^2 +8, then x >= 0

A: Proof using contraposition: If we want to prove "if A, then B", then using contrapositive statement…

Q: Prove A by Contradiction

A: Solution :-

Q: Prove that OfVg.dr = ] (Vfx Vg) · N ds.

A:

Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

Q: Let X-Bin(5,0.5), then P(X >3|X >2) is

A: Given information: Given that the random variable X follows binomial distribution with parameters n…

Q: Prove A X (BUC) - (Ax B) U (A x C)

A:

Q: Say whether the Runction is even, odd, or neither. Give reusans for your dnswer. go0 = x"+x-1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. Show that A is positive if and only if A B B for some B.

A:

Q: Prove that: ā x (B x č) = (ã-č )b – (ã ·5 )ẽ

A: See the details solution in below

Q: Prove: If a &lt; 0 and b &gt; 0, then | a  + b | &lt; | a | + | b |

A:

Q: The set of all positive multiples of v2 is countable.

A:

Q: - Show that (for n = 0, 1, 2, ..) (a) F(-n, b; c; 1) = - (c-b)n (c)n

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Let A = [0, 1] × [0, 1] C R². Suppose

A: (b) Given, A =0, 1×0, 1⊆ℝ2 and f : A → ℝ is continuous on A (relative to A)       Define F: 0, 1→ℝ…

Q: Show that if f : A → B and g : B → C are one-one, then gof : A → C is also one-one.

A: To show that the composition of two one to one function is also one to one.

Q: Let a = and b = . Find - à - b.

A: Given :a→=5, -5, -1b→=-4, 4, 0

Q: Prove that √2 is not an element of Q(?).

A:

Q: Show that a) A − ∅ = A. b) ∅ − A = ∅.

A:

Q: Prove: If a &gt; b, then a &gt; 1/2 ( a + b ) &gt; b.

A:

Q: R is commutative if and only if R[x] is Commutative. True or False

A: The given statement is true. If Rx is cummutative.So, R⊂RxRx is cummutative.R is also…

Q: Show that: If |z| = 1, then: |z3 + 4z + 5 < 5 z + 5z + 6

A: Given: z=1 Then show that z3+4z+5z2+5z+6≤5

Q: d) Show that whether 0 = Y is sufficient or not. max

A: Given function is: f(y)=1θ,      0≤y≤θ0,         elsewhere

Q: 3. Prove that (An B)² C A x B.

A:

Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: prove that if a>4 then (a-2)^2>4

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!