1. A=Z show if xRy <=> xy>=1 is reflexive, transitive and transitive. 2. A=Z show if...

1. A=Z show if xRy <=> xy>=1 is reflexive, transitive and transitive.

2. A=Z show if nRm <=> nm >= 0 is an equivalence relation and show the equivalence clases

3. A= R (real numbers) show if aRb <=> |a| = |b| is an equivalence relations and show the equivalence clases.

Expert Solution

Colby Messinger answered 1 year ago

Let R be a relation on a set that is reflexive and symmetric but not transitive?...

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For each of the properties reflexive, symmetric, antisymmetric, and transitive, carry out the following. Assume that...

For each of the properties reflexive, symmetric, antisymmetric, and transitive, carry out the following. Assume that R and S are nonempty relations on a set A that both have the property. For each of R complement (Rc), R∪S, R∩Sand R−1. determine whether the new relation must also have that property; might have that property, but might not; or cannot have that property. Any time you answer Statement i or Statement iii, outline a proof. Any time you answer Statement ii,...

For each of the properties reflexive, symmetric, antisymmetric, and transitive, carry out the following. Assume that...

For each of the properties reflexive, symmetric, antisymmetric, and transitive, carry out the following. Assume that R and S are nonempty relations on a set A that both have the property. For each of R complement, R∪S, R∩S, and R−1, determine whether the new relation must also have that property; might have that property, but might not; or cannot have that property. A ny time you answer Statement i or Statement iii, outline a proof. Any time you answer Statement...

Determine whether the relations described by the conditions below are reflexive, symmetric, antisymmetric or transitive on...

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Find each of the Definitions a. Transitive preferences b. Reflexive preference c. Marginal utility

1. For z=x^2-xy^2 find: a. the gradient for z; b. the directional derivative in direction of...

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2.) (12 pts.) Show that F = ( xy/(1+x^2y^2) + 1 + arctan(xy))i+ (x^2/(1+x^2y^2-1)j is a...

2.) (12 pts.) Show that F = ( xy/(1+x^2y^2) + 1 + arctan(xy))i+ (x^2/(1+x^2y^2-1)j is a conservative vector field. Then use the Fundamental Theorem for Line Integrals to find the Work done by F from point (0,0) to point (2, 1/2).

Argue with proof that whether following asymptotic notations are transitive, reflexive, or symmetric. O(n); o(n); Ω(n);...

Argue with proof that whether following asymptotic notations are transitive, reflexive, or symmetric. O(n); o(n); Ω(n); ω(n); ϴ(n)

Show complete solution 1. Show that the lines ?/1 = y+3/ 2 = z+1/3 and x-3/2...

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Question

1. A=Z show if xRy <=> xy>=1 is reflexive, transitive and transitive. 2. A=Z show if...

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Expert Solution

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