Question

give the correct reason for the question ​

Answer 1

Answer:

your answer is no. c

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Answer 2

Answer :

Option A

Solution :

Here ,

The given set is ;

{ 1 , 2 , 3 , 4 , 5 , 6 } = A (say)

Also ,

R = { (a , b) : b = a + 1 }

• If a = 1 , then b = 1 + 1 = 2

• If a = 2 , then b = 2 + 1 = 3

• If a = 3 , then b = 3 + 1 = 4

• If a = 4 , then b = 4 + 1 = 5

• If a = 5 , then b = 5 + 1 = 6

{ Note : We chose a = 1 , 2 , 3 , 4 , 5 . Because if a = 6 , then b = 6 + 1 = 7 ∉ A }

Hence ,

R = { (1 , 2) , (2 , 3) , (3 , 4) , (4 , 5) , (5 , 6) }

• R is not reflexive .

Reason :

(1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6) ∉ A

• R is not symmetric .

Reason :

(1,2) ∈ A but (2,1) ∉ A

(2,3) ∈ A but (3,2) ∉ A

(3,4) ∈ A but (4,3) ∉ A

(4,5) ∈ A but (5,4) ∉ A

(5,6) ∈ A but (6,5) ∉ A

• R is not transitive .

Reason :

(1,2) ∈ A and (2,3) ∈ A but (1,3) ∉ A

(2,3) ∈ A and (3,4) ∈ A but (2,4) ∉ A

(3,4) ∈ A and (4,5) ∈ A but (3,5) ∉ A

(4,5) ∈ A and (5,6) ∈ A but (4,6) ∉ A

Hence ,

R is neither reflexive nor symmetric nor transitive .

(Option A)