Question

1.Let A={0,1,2,3} Construct relations on A of the following types
i)not reflexive, not symmetric, not transitive
ii )not reflexive ,not symmetric, transitive
iii) not reflexive , symmetric ,not transitive
iv) not reflexive ,symmetric, transitive
V) reflexive, not symmetric, not transitive

Answer 1

Given:

A = {0, 1, 2, 3}

To find:

Construct relations on A of the following types

i)not reflexive, not symmetric, not transitive

ii )not reflexive ,not symmetric, transitive

iii) not reflexive , symmetric ,not transitive

iv) not reflexive ,symmetric, transitive

V) reflexive, not symmetric, not transitive

Soltion:

From given, we have, A = {0, 1, 2, 3}

(a, a) ∈ R → reflexive

(a, b) ∈ R and (b, a) ∈ R → symmetric

(a, b) ∈ R, (b, c) ∈ R ⇒ (c, a) ∈ R → transitive

i)not reflexive, not symmetric, not transitive

Let the relation R = { (3, 0), (2, 1), (0, 1) }

ii )not reflexive ,not symmetric, transitive

Let the relation R = { (3, 0), (2, 1), (0, 1), (1, 3) }

iii) not reflexive , symmetric ,not transitive

Let the relation R = { (3, 0), (2, 1), (0, 1), (1, 2) }

iv) not reflexive ,symmetric, transitive

Let the relation R = { (3, 0), (2, 1), (0, 1), (1, 2),  (1, 3)}

V) reflexive, not symmetric, not transitive

Let the relation R = { (3, 0), (2, 1), (0, 1), (1, 1) }

Answer 2

Answer:

Thanks for the answer

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