Math

Advanced MathQ&A Library1. Consider the following rules on the set of natural numbers, N, 1) write down 5ordered pairs of natural numbers that are related under the relation, and 2) decide forthe properties of reflexiveness (and irreflexiveness), symmetry (and antisymmetry) andtransitivity. Note: please specify explicitly whether the relation has each of the fiveproperties or not, and explain your answer."is less than or equal to"a factor of"c) "is 3 less than"Question

Asked Oct 18, 2019

61 views

Step 1

The 5 order pair of the natural number that is satisfy the relation “less than or equal to” as follows,

That means, if *a* and *b* are the natural number then it satisfy (*a *≤ *b*)

So, (1, 1), (1, 2), (2, 2), (2, 3), (1, 3)

When *a*, *b* and *c* belongs to the natural number or real number then,

If (*a*, *a*) or (*b*, *b*) or (*c*, *c*) ϵ N, then it reflexive.

If (*a*, *b*) ϵ N and also (*b*, *a*) ϵ N then it symmetry.

And, (*a*, *b*) ϵ N and (*b*, *c*) ϵ N then if (*a*, *c*) ϵ N, it is transitive.

Now, according to the above properties,

Since (1, 1) and (2, 2) are the reflexive. So the given relation is reflexive.

The above relation are not symmetric because *a* less than or equal to *b* but *b* not less than or equal to* a*.

Here, (1, 2) and (2, 3) and then also (1, 3) so the above relation is transitive.

Step 2

The 5 order pair of the natural number that is satisfy the relation “is a factor of” as follows,

That means, if *a* and *b* are the natural number then it satisfy (*a *factor of *b*)

So, (2, 4), (2, 6), (...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Use inductive reasoning and the data in the inclined plane time–distance table on page 12 to predict...

A: To recognize the pattern of numbers and determine the required number

Q: Use the indicated row operation to change matrix A, where T1 -2 -1 2 10 4 1 A 2 2 1 Add 7 times row ...

A: To perform the required row transformatin on the given (augmented) matrix

Q: Solve using the Method of Coefficients: y'' + 3y' + 2y = 7 cos x - sin x

A: The given differential equation

Q: To convert from gallons to quarts, multiply by what? 7 gallons: 28 quarts

A: From the given information, there are 7 gallons and 28 quarts.Obtain the number of gallons equal to ...

Q: A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the ma...

A: From the given information,The weight W = 24 pounds and gravity g = 32 ft / s2.The spring stretches ...

Q: In Exercises 15-19 find the general solution. 15. y3y +2y e3x(1 + x)

A: To find a (any) function y=y(x) satisfying the given non-homogeneous equation

Q: 20.

A: To prove that the additive group Z of integers has infinitely many subgroups H , each of which is is...

Q: Linear Alegebra: Show that the transformation t(x1,x2)=(2x1-2x2,9x1-8x2) is invertible, and find a f...

A: To prove that the given linear transformation is invertible and to find the inverze

Q: Exercise 9: Suppose we are given the following: lim f(x)3, lim g(x) 0, lim h(x) -2 C C Evaluate the ...

A: Hey, since there are multiple subparts posted, we will answer first 3 questions. If you want any spe...