For each of the following relations on the set {0, 1, 2, 3}. • r1 = {(0, , , , 3)} • r2 = {(1, , , 3)} • r3 = {(0, , , , , , 3)} • r4 = {(0, , , , , , 3)} (a) which of these relations are reflexive? (b) which of these are symmetric? (c) which of these are anti-symmetric? (d) which of these are transitive?

(a)  

(b)

(c)

(d)

Step-by-step explanation:

Since,

A relation R defined on A is called reflexive if,

∀ x ∈ A, (x, x)∈ R  

It is called symmetric,

∀ x, y ∈ A, if (x, y)∈ R then (x, y)∈ R such that x ≠ y,

It is called anti symmetric,  

∀ x, y ∈ A, if (x, y)∈ R then (x, y)∈ R such that x = y,

It is called transitive,

∀ x, y, z ∈ A, if (x, y)∈ R and (y, z)∈ R then (x, z)∈ R such that x ≠ y,

Given set,

{0, 1, 2, 3},

Also, the relation defined on the set are,

• = {(0, 0),(1, 1),(2, 2),(3, 3)}

• = {(1, 1),(2, 2),(3, 3)}

• = {(0, 0),(1, 1),(2, 0),(2, 2),(2, 3),(3, 3)}

• = {(0, 0),(0, 1),(1, 0),(1, 1),(2, 2),(3, 3)}

Hence, by the above explanation it is clear that,

Relations which are reflexive,

Relations which are symmetric,

Relations which are anti-symmetric,

Relations which are transitive,

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

answer: it's upside down and i can't read it

step-by-step explanation: