# Relation Question

• Jun 9th 2013, 06:29 AM
Relation Question
Relation R defined on the set of seven-bit strings by s1Rs2, provided that the first four bits of s1 and s2 coincide

(i) Show that R is anequivalence relation.

(iii) List one (1) member of each equivalence class.

• Jun 9th 2013, 07:25 AM
Plato
Re: Relation Question
Quote:

Relation R defined on the set of seven-bit strings by s1Rs2, provided that the first four bits of s1 and s2 coincide
(i) Show that R is an equivalence relation.
(iii) List one (1) member of each equivalence class.

Here coincide is synonymous with same as. As such almost all such relations are equivalence relations.

You post your efforts on showing the three required properties.

For the second part, there will be sixteen strings.
• Jun 9th 2013, 08:20 AM
Re: Relation Question
hey plato thanks for the reply, I just have a doubt here....if the first four bits coincide how about the rest three? how i want to proof in matrix form if i can't determine the rest three bits?
• Jun 9th 2013, 08:45 AM
Plato
Re: Relation Question
Quote:

hey plato thanks for the reply, I just have a doubt here....if the first four bits coincide how about the rest three? how i want to proof in matrix form if i can't determine the rest three bits?

The last three bits have nothing whatsoever to do with this question.
\$\displaystyle 1101000~R~1101111\$ but not \$\displaystyle 1100000~{R}~1101000\$ WHY?

In all of these strings , does each string have the same first four bits as itself? What property would that prove?
• Jun 9th 2013, 08:53 AM
Re: Relation Question
reflexive?
• Jun 9th 2013, 08:56 AM
Plato
Re: Relation Question
Quote:

reflexive?

Yes. Now you do the other two.
• Jun 9th 2013, 09:00 AM
Re: Relation Question
but is this relation valid

1101010 R 1101000?
• Jun 9th 2013, 09:11 AM
Plato
Re: Relation Question
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