If ƒ : R → R and g : R → R are both one-to-one, is f + g one-to-one? If f and g are both onto, is f + g onto?

Q: e) Does the equality |A U B| = |A| + |B| hold for every set A and B? f) Is it true that for any…

A:

Q: Suppose R and S are symmetric relations on a set A. Prove that RoS is symmetric iff RoS = So R.

A:

Q: Suppose f: A → B, f is one-to-one and onto, and Y c B. Show that the inverse image of Y under f and…

A: The function f is one-one and onto.   The function f is one-one if two different element in A…

Q: Suppose f: B → C and g: A → B are functions. Check all the statements that are true: A. If fog is…

A:

Q: Let A be the set of all permutations of the 26 letters in the English alphabet. The relation R on A…

A:

Q: Suppose S and T are infinite sets and φ: S→T is a function that is not onto. May we conclude that S…

A:

Q: Suppose that each of R ad T is a relation on a set A, the matrix for R is MB, and he matrix for T is…

A:

Q: With regard to composition of relations, If S and R are both anti-reflexive, then  s∘r is…

A: S&R both are anti- reflexive. Therefore There is no common elements in theses two sets.

Q: Question 11 Given domain of the relation R is {a}. R = {(a, a)} is a reflexive, symmetric and…

A: The domain of relation R is a.

Q: Let R be a relation on the set of all integers such that aRb if and only if a + b is even. Is R…

A:

Q: 1. Let A, B, and C be sets such that An Bn C + Ø. Draw a Venn diagram for each of the following set…

A:

Q: Let A = {x | 5x + 1 E Q} and B be the set of all even integers. Prove that A and B have the same…

A:

Q: If f:{1,2,3}->{a,b}, f(1)=a f(2)=b f(3)=a then explain why f is onto but not one to one

A:

Q: 1. Suppose R and S are symmetric relations on a set A. Prove that Ros is symmetric if Ros=SOR

A: Given:  To prove R and S are symmetric relations.

Q: 4. Let the relation R = { (a, b) e Z × Z l(a + b) = 1 (mod 5) }. a. Is the relation transitive?…

A: A relation R between two sets A and B is the set of all ordered pairs a,b such that a∈A and b∈B. We…

Q: Consider the relation on Z × Z given by aRb if a < b. Is R transitive. Answer yes or no…

A:

Q: . Define a relation R on Z as follows: a Rb if and only if 5 | (a²- 6²). Find four integers which…

A:

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

A: