Question

let A={3,5} and B={7,11}. let R={(a,b):a€A, b€B, a-b is odd.} show that, R is an empty relation from A into B.​

Answer 1

Answer:

Given:

A = (3, 5) and B = (7, 11)

Also,

R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}

a are the elements of A and b are the elements of B.

∴

a

−

b

=

3

−

7

,

3

−

11

,

5

−

7

,

5

−

11

∴a−b=3−7,3−11,5−7,5−11

⇒

a

−

b

=

−

4

,

−

8

,

−

2

,

−

6

⇒a−b=−4,−8,−2,−6

Here, a - b is always an even number

.

Here, a - b is always an even number.

So, R is an empty relation from A to B.

Hence proved.

Answer 2

Answer:

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Step-by-step explanation:

A={3,5}  B={7,11}

R=(a,b):a∈A,b∈B,a−b is odd.

Let B=7,a=3

b−a=4, which is even.

Each element of B is odd & A also has odd elements.

Hence a−b is never be odd, it will always negetive even no.

Hence R=(a,b)∈ϕ.