11. Let R and R' be two rings. A mapping f: R→R' is called an antihomomorphism, if f(x+y)=f(x) + f(y) and f(xy) =f(y)f(x) \ x, y = R. Let f, g be two antihomomorphisms of a ring R into R. Prove that fg: RR is a homomorphism.

Q: Proof of SAS Congruence Theorem.

A: I am attaching image so that you understand each and every step.

Q: Question: Prove if Card(A)B is an injection then g:P(A)->P(B). If f:A->B is an injection since A is…

A: Somewhat you are correct means your way and idea of thinking or correct need some proper proof. I…

Q: If ftickiieI{ is acollechion of Subsets ofX then く) andh %3D det the equality not (X;)-( true in…

A:

Q: Prove that if a, b e Z – {0}, then gcd(a, b) = gcd(a, -b)

A: Solution:-   gcd a,b= Greatest common divisor of  a  and  b ∗Every integer  that divides  a  and  b…

Q: he equivalence class of 3 for the relation congruence modulo 7 is given by O [7], =…

A: The congruence class of 3 for the relation : congruence modulo 7 is given by,

Q: Use the definition of an r-permutation, or the product rule to determine the number of trifectas…

A: the product rule to determine the number of trifectas possible in a race with 9 horses. A trifecta…

Q: If sup(S) exists, then it is unique ylgn ihi

A: The solution is given as

Q: DATE I OBJECT (5-15) let A,B,C,D be subsets of asetU show that An(AnB')-Ø

A:

Q: Express (123456789)

A:

Q: Fallacy of induction and its types with examples

A: Fallacy of weak induction and its types with examples Appeal to ignorance some  times the best…

Q: There erists a finite Propositic collection (A;)jeJ of disjoint subsets of R, such that m (UA; +Em"…

A:

Q: bounded Decide unbounded the doma n

A: (As per bartleby guidelines, for questions containing multiple subparts, only first three subparts…

Q: What is the domain of the following: {(3,4), (9,1), (10, 5), (2, 15), (8,4)} O {3,4,9, 1, 10, 5, 2,…

A: Domain of a function: The domain of a function fx is the set of all values of x for which the…

Q: The following is a proof that ``For all sets A and B, P(An B) ≤ P(A) ʼn P(B)". Fill in the blanks.…

A:

Q: What is the degree of the recurrence relation an+1 -4an+3-an-1=0 ? (1) 1 (2) 4 (3) 3 (4) 2 A) Choice…

A:

Q: Let R be a relation on the set of all non-negative integers defined by aRb if and only if a3 - b3 is…

A:

Q: Every first countable space has a local countable base.

A:

Q: Let A = {Ba: a € A} be a family of sets and let G be a nonempty set. Prove Gn an (UB.) - U(GOB₂) =…

A: Given: A=Bα : α∈∆ be a family of sets and let G be a nonempty set. To prove: G∩∪α∈∆Bα=∪α∈∆G∩Bα

Q: 2. (~P-Q) – (~P – -Q) Q -P -P+Q -P - "Q (-P - Q) - (-P- -Q)

A: P→Q is False if and only if P is True and Q is False P↔Qis False if and only if one is True and…

Q: Punctian diffexentiable Af not Is every in tegsable. by then prove it giving countes example.

A: No, every differentiable function is not Integrable. Consider the function f(x)=1x  in (0,1). Obtain…

Q: 5. (1) Show that the lexicographical order on {0, 1}x N with the standard orders on {0, 1} and on N…

A: Lexicographical order on with the standard orders on .Also, is the ordinal of  with the standard…

Q: Consider the following subset of R": W = {(x1,x2, 83, L4, 25) E R° | r1 = x2 = 13, 14 + 15 = 0}. (a)…

A:

Q: Copy 13 Let L₁ and L2 be two languages over the alphabet \Sigma = (a, b, c), defined as follows. L1…

A: (A) Grammar G1 that generates L1:The grammar G1 for generating L1 can be defined as follows:1.Set of…

Q: QUESTION 1 Is relation R on set of all integers reflexive where (x,y) ER if x is a multiple of y?…

A:

Q: How many ways are there to select two subsets A and B of {1,2,…,n} such that A and B are {\em not}…

A: Both A and B must be non-empty. So, possible cardinality of A can be  1,2,3, ..., n-1.

Q: When are ~o attributesJaid to be positively assOCiated and nep'tive1y associated? Also define…

A: In the theory of attributes , the attributes A and B are said to be associated with each other only…

Q: öalg älbäi = For the figure shown, f(2) .2 2

A: We have to find f(2)

Q: Define dircect proof

A: Direct proof: a direct proof is a way of showing the truth or falsity of a given statement by a…

Q: Consider the set L:= {(a,b) E Z²| (a – b) is a multiple of 3}. A proposed recursive definition for L…

A: Consider the provided question. L=a,b∈L'a-b is multiple of 3 therefore, a-b=3ka=b+3k  where k is an…

Q: how to use Bolzano Weierstrass Theorem to prove that every bounded infinite subset has at least one…

A:

Q: What is the domain of the following {(3,4), (9,1), (10,5), (2,15), (8, 4)} O {3, 4, 9, 1, 10, 5, 2,…

A: We know that for a pointx,y is domain is x and range is y Similarly, for given…

Q: Please poove 18 ŏ bound of (३5) fश्ठ also proove ppes an sup13,5)%35

A: (.) Upper bound:    "A number that is greater than or equal to any number in a non-empty subset of ℝ…