Question

Prove the following: Theorem. Let R ⊆ X × Y and S ⊆ Y × Z...

Prove the following: Theorem. Let R ⊆ X × Y and S ⊆ Y × Z be relations. Then

1. Range(S ◦ R) ⊆ Range(S), and

2. if Domain(S) ⊆ Range(R), then Range(S ◦ R) = Range(S)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
5. Prove or disprove the following statements: (a) Let R be a relation on the set...
5. Prove or disprove the following statements: (a) Let R be a relation on the set Z of integers such that xRy if and only if xy ≥ 1. Then, R is irreflexive. (b) Let R be a relation on the set Z of integers such that xRy if and only if x = y + 1 or x = y − 1. Then, R is irreflexive. (c) Let R and S be reflexive relations on a set A. Then,...
Prove: Let x,y be in R such that x < y. There exists a z in...
Prove: Let x,y be in R such that x < y. There exists a z in R such that x < z < y. Given: Axiom 8.1. For all x,y,z in R: (i) x + y = y + x (ii) (x + y) + z = x + (y + z) (iii) x*(y + z) = x*y + x*z (iv) x*y = y*x (v) (x*y)*z = x*(y*z) Axiom 8.2. There exists a real number 0 such that for all...
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a)...
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a) Explain why R is not an equivalence relation. b) Explain why S is not an equivalence relation. c) Find S ◦ R. d) Show that S ◦ R is an equivalence relation. e) What are the equivalence classes of S ◦ R?
Prove that the set S = {(x, y, z) ∈ R 3 : x + y...
Prove that the set S = {(x, y, z) ∈ R 3 : x + y + z = b}. is a subspace of R 3 if and only if b = 0.
Prove the following theorem: Theorem. Let a ∈ R and let f be a function defined...
Prove the following theorem: Theorem. Let a ∈ R and let f be a function defined on an interval centred at a. IF f is continuous at a and f(a) > 0 THEN f is strictly positive on some interval centred at a.
Using field and order axioms prove the following theorems: (i) Let x, y, and z be...
Using field and order axioms prove the following theorems: (i) Let x, y, and z be elements of R, the a. If 0 < x, and y < z, then xy < xz b. If x < 0 and y < z, then xz < xy (ii) If x, y are elements of R and 0 < x < y, then 0 < y ^ -1 < x ^ -1 (iii) If x,y are elements of R and x <...
Let x, y ∈Z. Prove that (x+1)y^2 is even if and only if x is odd...
Let x, y ∈Z. Prove that (x+1)y^2 is even if and only if x is odd and y is even.
Let T: R^3----> R^3 where T(x,y,z) = (x-2z,y+z,x+2y) . Is T a one-to-one transformation? Is the...
Let T: R^3----> R^3 where T(x,y,z) = (x-2z,y+z,x+2y) . Is T a one-to-one transformation? Is the range of T R^3 ? Explain
(a) Let f(z) = z^2. R is bounded by y = x, y= -x and x...
(a) Let f(z) = z^2. R is bounded by y = x, y= -x and x = 1. Find the image of R under the mapping f. (b)Find the all values of (-i)^(i) (c)Find the all values of (1-i)^(4i)
Let R be an integral domain. Prove that R[x] is an integral domain.
Let R be an integral domain. Prove that R[x] is an integral domain.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT