Question

solve questions no 19 only .​

Answer 1

Ques: 19

Answer: the number of elements in A∩B is 6.

Given:

A = { (a, b) : a² + 3b² = 28, a, b∈Z }

Thus, A = { (5,1), (-5, -1), (5, -1), (-5,1), (4,2), (-4,-2), (4,-2), (-4,2),(1,3), (-1,-3), (1,-3), (-1,3) }

Also, given that:

B = { (a, b) : a>b, a, b ∈ Z }

∴A∩B = {(1,3), (-1,3), (-4,-2), (-4,2), (-5,-1), (-5,1) }

∴ The number of elements in A∩B is 6.

Brainliest plz!!

Answer 2

A = {(a,b) : a² + 3b² = 28, a,b∈Z}

B = {(a,b) : a > b, a,b∈Z}

We need to find number of elements in A∩B

Let us substitute values for 'b' and find 'a' using equation given in set A

Let b = ±1

a = ±5

Let b = ±2

a = ±4

Let b = ±3

a = ±1

We take only those values which satisfy a > b, we get

A∩B = {(5,1) , (5,-1) , (4,2) , (4,-2) , (1,-3) , (-1,-3)}

So A∩B has 6 elements