Discrete Math. Show all steps clearly
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Discrete Math. Show all steps clearly
Define a relation R on the set of all integers...
5. On the set of integers Z define the following relation: "aRb if and only if...
5. On the set of integers Z define the following relation: "aRb if and only if a - b is a multiple of 7." (1) Prove that R is an equivalence relation. 16 Marks] How many elements are there in the quotient set of 2 with respect to the equivalence relation R? Give reasons. |4 Marks
16. (8 points) Let Z be the integers and let A - Zx Z. Define the relation R on A by (a, b) R(c, d) if and only if a c and b 3 d for all (a, b), (c, d)E A. Prove that R is a partial ordering on A tha...
16. (8 points) Let Z be the integers and let A - Zx Z. Define the relation R on A by (a, b) R(c, d) if and only if a c and b 3 d for all (a, b), (c, d)E A. Prove that R is a partial ordering on A that is not a total ordering.
16. (8 points) Let Z be the integers and let A - Zx Z. Define the relation R on A by (a, b)...
Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of...
Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of counting nuobors and the relation {(X Z〉 | Ye F and Z € Fand y-2). This relation is just a version of the usual subset relation, but restricted to only apply to the sets in F Prove: CFis a partial order. Prove: Cis not symmetric and connected. Prove: If R is an equivalence relation, it is also a euclidean...
4) Let D be the set of all finite subsets of positive integers. Define a function...
4) Let D be the set of all finite subsets of positive integers. Define a function (:2 - D as follows: For each positive integer n, f(n) =the set of positive divisors of n. Find the following f (1), f(17) and f(18). Is f one-to-one? Prove or give a counterexample.
number theory and discrete math show full steps Find Gaussian integers a+ib and r+is such that...
number theory and discrete math
show full steps
Find Gaussian integers a+ib and r+is such that 234212 + 3421 i - (23+ 41i) (a + bi) + (r + si) such that 2 (72 +82) < 232 + 412.
10. (10 points) Define a relation on Z by setting x R y if xy is...
10. (10 points) Define a relation on Z by setting x R y if xy is even. a. Give a counterexample to show that is not reflexive. b. Give a counterexample to show that R is not transitive.
need help with proving discrete math HW, please try write clearly and i will give a thumb up thanks!! Let A and be B be...
need help with proving discrete math HW, please try write
clearly and i will give a thumb up thanks!!
Let A and be B be sets and let f:A B be a function. Define C Ax A by r~y if and only if f(x)f(y). Prove thatis an equivalence relation on A. Let X be the set of~-equivalence classes of A. L.e. Define g : X->B by g(x) Prove that g is a function. Prove that g is injective. Since g...
(10) Define a relation R on Zn (the integers mod n) as follows: lal isR related...
(10) Define a relation R on Zn (the integers mod n) as follows: lal isR related to [b (i.e. [an Rbn) iff there is [cn E Gn such that a b (a) Show that R is an equivalence relation on Zn (b) Give all the equivalence classes for R when n-12.
This problem is dealing with Discrete Math. Please answer fully and clearly, and show/explain all...
This problem is dealing with Discrete Math. Please answer fully
and clearly, and show/explain all steps or proofs that you state in
the answer.
4. Let (G, w) be a connected graph with weights on edges so that all weights are distinct positive real numbers. Suppose we find a MST (minimum spanning trees ) in G by using Prim's algorithm. Prove that no matter what vertex we begin with in Prim algorithm, the set of all weights on edges in...
Define a relation < on Z by m <n iff |m| < |n| or (\m| =...
Define a relation < on Z by m <n iff |m| < |n| or (\m| = |n| 1 m <n) (a) Prove that < is a partial order on Z. (b) A partial order R on a set S is called a total order (or linear order) iff (Vx, Y ES)(x + y + ((x, y) E R V (y,x) E R)) Prove that is a total order on Z. (c) List the following elements in <-increasing order. –5, 2,...
5. On the set of integers Z define the following relation: "aRb if and only if a - b is a multiple of 7." (1) Prove that R is an equivalence relation. 16 Marks] How many elements are there in the quotient set of 2 with respect to the equivalence relation R? Give reasons. |4 Marks
16. (8 points) Let Z be the integers and let A - Zx Z. Define the relation R on A by (a, b) R(c, d) if and only if a c and b 3 d for all (a, b), (c, d)E A. Prove that R is a partial ordering on A that is not a total ordering.
16. (8 points) Let Z be the integers and let A - Zx Z. Define the relation R on A by (a, b)...
Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of counting nuobors and the relation {(X Z〉 | Ye F and Z € Fand y-2). This relation is just a version of the usual subset relation, but restricted to only apply to the sets in F Prove: CFis a partial order. Prove: Cis not symmetric and connected. Prove: If R is an equivalence relation, it is also a euclidean...
4) Let D be the set of all finite subsets of positive integers. Define a function (:2 - D as follows: For each positive integer n, f(n) =the set of positive divisors of n. Find the following f (1), f(17) and f(18). Is f one-to-one? Prove or give a counterexample.
number theory and discrete math
show full steps
Find Gaussian integers a+ib and r+is such that 234212 + 3421 i - (23+ 41i) (a + bi) + (r + si) such that 2 (72 +82) < 232 + 412.
10. (10 points) Define a relation on Z by setting x R y if xy is even. a. Give a counterexample to show that is not reflexive. b. Give a counterexample to show that R is not transitive.
need help with proving discrete math HW, please try write
clearly and i will give a thumb up thanks!!
Let A and be B be sets and let f:A B be a function. Define C Ax A by r~y if and only if f(x)f(y). Prove thatis an equivalence relation on A. Let X be the set of~-equivalence classes of A. L.e. Define g : X->B by g(x) Prove that g is a function. Prove that g is injective. Since g...
(10) Define a relation R on Zn (the integers mod n) as follows: lal isR related to [b (i.e. [an Rbn) iff there is [cn E Gn such that a b (a) Show that R is an equivalence relation on Zn (b) Give all the equivalence classes for R when n-12.
This problem is dealing with Discrete Math. Please answer fully
and clearly, and show/explain all steps or proofs that you state in
the answer.
4. Let (G, w) be a connected graph with weights on edges so that all weights are distinct positive real numbers. Suppose we find a MST (minimum spanning trees ) in G by using Prim's algorithm. Prove that no matter what vertex we begin with in Prim algorithm, the set of all weights on edges in...
Define a relation < on Z by m <n iff |m| < |n| or (\m| = |n| 1 m <n) (a) Prove that < is a partial order on Z. (b) A partial order R on a set S is called a total order (or linear order) iff (Vx, Y ES)(x + y + ((x, y) E R V (y,x) E R)) Prove that is a total order on Z. (c) List the following elements in <-increasing order. –5, 2,...
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