Question

Help!! what are the differences between 'necessary condition' and 'sufficient condition'?

Answer 1

the former may be used to denote optimal condition, the other as minimum. I hope this helps

Answer 2

the former may also be used to denote necessity, and the latter adequateness to fullfil a requirement

Answer 3

is this a math question?

Answer 4

a logical question then: so I am right on the second one.

Answer 5

Consider two conditions x^2-3x-10<0 and abs(x-2) < 'a' on a real number x, where 'a' is a positive real number.
Q1 : What is the range of values of 'a' such that abs(x-2)<'a' is a necessary condition for x^2-3x-10<0.
Q2 : What is the range of values of 'a' such that abs(x-2)<'a' is a sufficient condition for x^2-3x-10<0.

Answer 6

panlac01 : see the question? help plz

Answer 7

but the answer is a>=4

Answer 8

i just don't understand

Answer 9

and the sufficient condition is 0<a<=3

Answer 10

but it was wrong from answer key

Answer 11

Definition: A necessary condition for some state of affairs S is a condition that must be satisfied in order for S to obtain.

For example, a necessary condition for getting an A in 341 is that a student hand in a term paper. This means that if a student does not hand in a term paper, then a student will not get an A, or, equivalently, if a student gets an A, then a student hands in a term paper.

Definition: A sufficient condition for some state of affairs S is a condition that, if satisfied, guarantees that S obtains.

For example, a sufficient condition for getting an A in 341 is getting an A on every piece of graded work in the course. This means that if a student gets an A on every piece of graded work in the course, then the student gets an A.

Answer 12

Here's some examples that may help:-
If I hit my china tea cup with a hammer it will break.
If I drop my chine tea cup on a stone floor it will break.
Both of these are then SUFFICIENT conditions for me to end up with a broken tea cup BUT neither is NECESSARY because there are lots of ways to break a tea cup.
If I eat good food I should stay healthy
If I take regular exercise I should stay healthy
Both of these are NECESSARY conditions for me to remain healthy but neither is SUFFICIENT as I have to do both to stay healthy - and quite a few other things as well like avoiding disease.
Hope that helps!

Answer 13

First work out the conditions for the quadratic to be below 0 i.e. below the x-axis if you draw a graph. x^2-3x-10 = (x+2)(x-5) so x must be between -2 and 5. Now work out all the values |x-2| can take: |5-2| =3 etc. You'll find that the maximum value is when x = -2 i.e. |-2-2| = 4. So so long as 'a' is greater or equal to 4 it's GUARANTEED that x can take all the values it needs for x^2-3x-10 < 0. Thus we say it's NECESSARY for this condition to hold. For the SUFFICIENT condition we just want the values of |x-2| to sneak in so that x^2-3x-10 < 0. At one end x = 5 so |x-2| = 3 and at the other when x = 2 |x-2| = 0 hence the SUFFICIENT condition that 0<a<=3. Good Luck!

Answer 14

@JohnMartin: may u explain SUFFICIENT condition clearer? thk in advance.

Answer 15

I meant why we use x=5 and x=2, how abt x=-2?

Answer 16

Sorry Otonashi I'd forgotten what the question was and now I see what the problem is. If you look back at the maths question you asked you'll see that 'a' must be a positive integer so it HAS to be > 0. In other words 0 < a is the same thing as 0 < |x-2| which would make x > 2 - I was wrong to say = first time. And this HAS to be there because just saying a <= 3 (so it just sneaks in on the upper limit) would imply that 'a' could be -1000 which would be clear rubbish as the abs of anything can't be negative. I hope that helps!

Answer 17

Thank you so much.
Uh-no...
Can sufficient condition be 0<a<4? ^^

Answer 18

No the sufficient condition isn't 0<a<4 because the range of this answer is too great. Remember that sufficient means "just enough". If you draw a graph of the original quadratic x^2-3x-10 then you'll see that to be < 0 x must be between -2 and 5. When x is 5 'a' (which is |x-2|) is 3. At the other end when x is -2 'a' is 4. But we want the smallest range - the one thats 'just enough' - so we choose 'a' < 3 as this is all that is required to sneak into the < 0 area for the quadratic. Good luck!

Answer 19

thanks :)