Question

Let A = {x ∈ Z | x = 5a+2 for some integer a}, B =...

Let A = {x ∈ Z | x = 5a+2 for some integer a}, B = {x ∈ Z | x = 10b−3 for some integer b}. Prove or disprove the statements. 1. A ⊆ B 2. B ⊆ A

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A 4 c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
Let a be prime and b be a positive integer. Prove/disprove, that if a divides b^2...
Let a be prime and b be a positive integer. Prove/disprove, that if a divides b^2 then a divides b.
Let Z be the integers. (a) Let C1 = {(a, a) | a ∈ Z}. Prove...
Let Z be the integers. (a) Let C1 = {(a, a) | a ∈ Z}. Prove that C1 is a subgroup of Z × Z. (b) Let n ≥ 2 be an integer, and let Cn = {(a, b) | a ≡ b( mod n)}. Prove that Cn is a subgroup of Z × Z. (c) Prove that every proper subgroup of Z × Z that contains C1 has the form Cn for some positive integer n.
2. Define a function f : Z → Z × Z by f(x) = (x 2...
2. Define a function f : Z → Z × Z by f(x) = (x 2 , −x). (a) Find f(1), f(−7), and f(0). (b) Is f injective (one-to-one)? If so, prove it; if not, disprove with a counterexample. (c) Is f surjective (onto)? If so, prove it; if not, disprove with a counterexample.
Prove or disprove the following statements. a) ∀a, b ∈ N, if ∃x, y ∈ Z...
Prove or disprove the following statements. a) ∀a, b ∈ N, if ∃x, y ∈ Z and ∃k ∈ N such that ax + by = k, then gcd(a, b) = k b) ∀a, b ∈ Z, if 3 | (a 2 + b 2 ), then 3 | a and 3 | b.
Let X = { x, y, z }. Let the list of open sets of X...
Let X = { x, y, z }. Let the list of open sets of X be Z1. Z1 = { {}, {x}, X }. Let Y = { a, b, c }. Let the list of open sets of Y be Z2. Z2 = { {}, {a, b}, Y }. Let f : X --> Y be defined as follows: f (x) = a, f (y) = b, f(z) = c Is f continuous? Prove or disprove using the...
Let G=Z x Z and H={ (a, b) in Z x Z | 8 divides (a+b)...
Let G=Z x Z and H={ (a, b) in Z x Z | 8 divides (a+b) }. 1. Prove that G/H is isomorphic to Z8. 2. What is the index of [G : H]? Explain.
Prove or disprove (a) Z[x]/(x^2 + 1), (b) Z[x]/(x^2 - 1) is an Integral domain. By...
Prove or disprove (a) Z[x]/(x^2 + 1), (b) Z[x]/(x^2 - 1) is an Integral domain. By showing (a) x^2+1 is a prime ideal or showing x^2 + 1 is not prime ideal. By showing (b) x^2-1 is a prime ideal or showing x^2 - 1 is not prime ideal. (Hint: R/I is an integral domain if and only if I is a prime ideal.)
1)Let ? be an integer. Prove that ?^2 is even if and only if ? is...
1)Let ? be an integer. Prove that ?^2 is even if and only if ? is even. (hint: to prove that ?⇔? is true, you may instead prove ?: ?⇒? and ?: ? ⇒ ? are true.) 2) Determine the truth value for each of the following statements where x and y are integers. State why it is true or false. ∃x ∀y x+y is odd.