If C ={}    is {} an element of c

Q: 2. Let A Ø. If A has exactly n elements, then A has exactly 2" subsets, Vn € N.

A: A is non empty subset of n elements ,then A has exactly 2n subsets,∀n∈ℕ.

Q: (iv) The power set P(C) of C by listing down the elements directly.

A:

Q: 2 Let o (1 3 5)(2 4) and T (1 5)(2 3) be elements of S. Find o,or,to, and to

A: Note: Here the operation is composition of permutation group S3.

Q: If ∠A≡∠C in ABCD, then ABCD is cyclic.

A:

Q: Prove that if A ⊂ B and B ⊂ C, then A ⊂ C

A: Given problem is :   Prove that if A ⊂ B and B ⊂ C, then A ⊂ C.

Q: 10

A:

Q: Prove that A C B if and only if B C Ā.

A: A set X is said to be a subset of another set Y, if every element in set X is also an element in set…

Q: 3. Use the Racetrack Principle to show that: In x 1

A: The Racetrack Principle :-

Q: a b = a - b is a commutative binanry operation on Z

A: Commutative operation means without changing the operation the values doesn't change.

Q: Suppose a and ß are transpositions, then show that if aß= (1), then a = B.

A:

Q: Represent in the Argand Diagram all such z for which |z + 13| < 15

A:

Q: 2. Suppose a, b, and care integers. Prove that if a |band alethen a |b+c and a|b-c.

A: Assume a|b and a|c.

Q: Prove that if A – B – D and B – C – D, then A -C– D.

A:

Q: Let zC LC and ZPOC ZP'O'C. 0" 0.

A: To find: The correct statement. Given information: ∠C≅∠C' and ∠POC≅∠P'O'C' Let O'' be a point on CO…

Q: d. a specific element of R° that is not in V. е. a specific element of v in V for which -v is not in…

A: Given (a,b,c) where c=a-2b

Q: If X(z) = In(z - 2), then what's x(k) а. O b. ak O C. -ak / k d. others е. ak / k

A: Z transform and inverse Z transform

Q: Apply any method to prove that if a|b and alc then a|(bc – 3c)

A: We will use direct proof method to prove the given statement

Q: Given d, = and dy = Then d, and d, are not - conjugateif Non of these O D

A: Given d0 = -11  and  d1 = 56

Q: Prove this: A≤B iff AnB=A

A:

Q: 4. (a) Write down four distinct elements of the set {2 €C:2- E = 2i}.

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Prove that if a|b and b|c, then a|c.

A:

Q: Prove that if n 2 3, the only element o of S, satisfying oy =ya for all y E S, is the identity…

A: Let n≥3. Let σ∈Sn such that σγ=γσ for all γ∈Sn. Suppose σ≠i, the identity Then there exists…

Q: The_____ of A and B consists of all elements in either A or B or both.

A: The_____ of A and B consists of all elements in either A or B or both.   The answer of the above…

Q: If n is not a poime then there exist Some ab€ 7h Such that ab # Itnk fox all

A: Definition: A number which can not be factored as product of two numbers other than the number…

Q: 2. Let A = and B = al. Show that det(A + B) = det A + det B if and only if a + d = 0.

A:

Q: Let {0, 1}N = {(a, a1, a2, . ..) : an = 0 or 1, n E N}. • Construct a 1-1 correspondence between {0,…

A: let 0,1N=a0,a1,a2,....:an=0 or 1, n∈ℕ (i) construct a 1-1 correspondence between 0,1ℕ and all the…

Q: Let A = a22 Show that if d = a¡|a» – A2jɑ12 # 0, then 1 A- = a22 -a12

A:

Q: if and only if |z| =3 vlgn

A: True

Q: Answer the following questions about a deli system in a grocery store. Within the system, every…

A: (a) The customer IDs are ranging from p to q  inclusive. and meats with IDs ranging from r to s,…

Q: If a z 0, then |a If a < 0, then |a||

A: if a&gt;=0, |a| = ?  if a&lt;0, |a| = ?

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

A:

Q: If z = eax+by az then a az is ay

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Let a that Note: 1 6- a

A: we have been given that the function f is a continuous function. So, first, we will define the…

Q: Compute |A| for the following:

A: Given: A=234124431

Q: Prove: If A ∪ C = B and A ∪ D = B and A ∩ C = ∅ and A ∩ D = ∅, then C=D.

A:

Q: if C={}         is {} subset of C ?

A: Question: Is the empty set a subset of itself?

Q: What is i in element a32?

A:

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

A:

Q: Suppose |A| = |B|. Prove that |P(A)| = |P(B)|

A: Given that |A|=|B| We need to prove that |P(A)|=|P(B)| Since, |A|=|B|, then there is a bijection ,…

Q: If A is a subset of a me

A: Given is a matric space X and a subset A. Then it is needed to prove that  A=x: each open sphere…

Q: Prove that if A C B then P(A) C P(B).

A: Proof:

Q: If X(z) = In(z - 2), then what's x(k) a. -ak / k b. -ak С. aк d. others e. ak /k

A: Inverse Z transform found using multiplication by k property

Q: Every subset of S is uncountable.

A:

Q: How to solve this?

A:

Q: a. If A and B are independent, and A and B are independent, show that A and B are also independent.

A:

Q: If X(z) = In(z - 2), then what's x(k O a. -ak O b. ak O c. -ak /k O d. others Oe. ak / k O O

A: Given that X(z) = ln(z - 2) We have to find the value of X(k).