Let A = { − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , } . L e tR be a relation on A defined by x R y if and only if 0 ≤ x 2 + 2 y ≤ 4 . Let l be the number of elements in R and m be the minimum number of elemen

Question

Let A = { − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , } . L e tR be a relation on A defined by x R y if and only if 0 ≤ x 2 + 2 y ≤ 4 . Let l be the number of elements in R and m be the minimum number of elements required to be added in R to make it a reflexive relation. then l + m is equal to

TestHub · Accepted Answer

​ A = { − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 } − 2 y ≤ x 2 ≤ 4 − 2 y ​ y = − 3 y = − 2 y = − 1 y = 0 y = 1 y = 2 y = 3 ​ 6 ≤ x 2 ≤ 10 4 ≤ x 2 ≤ 8 2 ≤ x 2 ≤ 6 0 ≤ x 2 ≤ 4 − 2 ≤ x 2 ≤ 2 − 4 ≤ x 2 ≤ 0 − 6 ≤ x 2 ≤ − 2 ​ ⇒ x ∈ { − 3 , 3 } ⇒ x ∈ { − 2 , 2 } ⇒ x ∈ { − 2 , 2 } ⇒ x ∈ { − 2 , − 1 , 0 , 1 , 2 } ⇒ x ∈ { − 1 , 0 , 1 } ⇒ x ∈ { 0 } ⇒ No x -Exist ​ ​ R = {( − 3 , − 3 ) ( − 3 , 3 ) , ( − 2 , − 2 ) ( − 2 , 2 ) ( − 1 , − 2 ) ( − 1 , 2 ) ( 0 , − 2 ) ( 0 , − 1 ) ( 0 , 0 ) ( 0 , 1 ) ( 0 , 2 ) ( 1 , − 1 ) ( 1 , 0 ) ( 1 , 1 ) ( 2 , 0 )} ∴ ℓ = 15 ​ To make it reflexive we will add ​ {( − 1 , − 1 ) , ( 2 , 2 ) , ( 3 , 3 )} ∴ m = 3 ∴ ℓ + m = 15 + 3 = 18 ​

Mathematics - Sets and Relations Question with Solution | TestHub

Options:

Doubts & Discussion