Assignment Task:
Introduction to Binary Relations IT Assignment Help 

Question 1
Let’s consider the following congruence modulo 5 relation R, defined from the set of integers, Z to the set of integers Z as follows:

m R n ⇐ ⇒ 5|(m − n)

(a) Is 26 R 1? Please explain why or why not.

(b) Is (9, 3) ∈ R? Please explain why or why not.

(c) Is (57, 32) ∈ R? Please explain why or why not.

(d) List five integers n such that n R 2.

(e)List five integers n such that 27 R n.

Question 2
Le tA be the set of all strings of a js and b
js of length 7. Let’s define a relation R onA as follows: For all s,t ∈ A, s R t ⇐⇒ s and t have the first character, and the last two characters in common (the same).

(a) Is abaaaba R abbaaba?

(b) Is aabbaab R bbaabba?

(c) Is aaaaaaa R aaabaaa?

(d) Define another pair of 7-character strings from the alphabet (a,b) that satisfy the given relationship R.

(e)Define another pair of 7-character strings from the alphabet (a,b) that do not satisfy the given relationship R.

 

Question 3
Let R be the relation {(1,3),(1,4),(2,3),(2,4),(2,7)}, and let S be the relation {(3,5),(4,5),(3,6),(4,6)}. Find the composition S ? R.

Question 7
Let Abe a Cartesian product Z×Z, and let F be a relation defined on Aas follows:
For all (x1, y1) and (x2, y2) ∈ A : (x1, y1) F (x2, y2) ⇐⇒ x1 = x2
Pleaseshowyourwork to determine whether or not the given relationis:
(a)Reflexive:

(b)Symmetric:

(c)Anti-symmetric:

(d)Transitive:

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  • Posted on : November 21st, 2018

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