What are the necessary and sufficient conditions for inequalities?

Answer 1

Posted by ILias

1. The problem statement, all variables and given/known data

consider two conditions x2-3x-10 < 0 and |x-2| < A on a real number x, where A is positive real number

(i) find the range of values of A such that |x-2| < A is a necessary condition for x2-3x-10 < 0

(ii) find the range of values of A such that |x-2| < A is a sufficient condition for x2-3x-10 < 0

2. Relevant equations

3. The attempt at a solution

what is necessary and sufficient condition? I tried googling but found nothing about it...

thanks

Well, the first step is to solve the equality x2-3x-10= 0. You will get two solutions. Then you will have to think about what makes the inequality true. The necessary condition is the one that is required to make the statement true: "For Hot Dogs to taste good, they must have mustard". The sufficient condition is the one that says if the condition is met, the statement is true, "As long as hot dogs have mustard, hot dogs are good." The necessary and sufficient condition that if that condition is met, by necessity, the statement is true "only hot dogs that have mustard are good (necessity) and if they have mustard they need nothing else to be good (sufficiency)".