Let S = x ∈ - 6 , 3 - - 2 , 2 : x + 3 - 1 x - 2 ≥ 0 and T = x ∈ Z : x 2 - 7 x + 9 ≤ 0 . Then the number of elements in S ∩ T is

Step-by-step solution

Given, x 2 - 7 x + 9 ≤ 0 ⇒ x ≤ 7 ± 13 2 ⇒ x ∈ 7 - 13 2 , 7 + 13 2 Also given x ∈ Integers , so x can be ± 2 ,   ± 3 ,   ± 4 ,   ± 5 Now out of these values of x only 3 ,   - 4 ,   - 5 will satisfy S = x + 3 - 1 x - 2 ≥ 0 So, S ∩ T ∈   3 ,   - 4 ,   - 5 So, n S ∩ T = 3