Question

Let z be the set of all integers and
A = {(a, b) : a2 + 3b2 = 28, a, b e Z}
B = {(a, b): a > b, a, b e Z}, then n(
AB) is equal to
(1) 1
(2) 6
(3) 3
(4) 8​

Answer 1

Answer:

(2) 6

Step-by-step explanation:

A={(a,b):a

2

+3b

2

=28,a,b∈Z}

={(5,1),(−5,−1),(5,−1),(−5,1),(4,2),(−4,−2),(4,−2),(−4,2),(1,3),(−1,−3),(1,−3),(−1,3)}

and 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.