Can Inequalities be Proven with Simple Algebraic Manipulation?

[elle]

Hi, can someone help me with the following question? I don't know how to approach the proof

If a < b and c < d then ac < bd is true, supply a proof.

Thanks!

 

[Fermat]

Hi, can someone help me with the following question? I don't know how to approach the proof
If a < b and c < d then ac < bd is true, supply a proof.
Thanks!

It's not true !

let a = -2, b= -1 then a < b is true
let c = 0, d = 1 then c < d is true
but
ac = -2*0 =0
bd = -1*1 = -1
and
0 not < -1
so
ac < bd is not true

if a,b,c,d are all positive, then the statement is true

 

[elle]

Oh so if a,b,c and d are all real numbers, does that mean the statement is true? How do I approach the proof

 

[Gokul43201]

elle, do you know what a real number is ? I think you mean 'positive numbers.'

In any case, if the question is exactly as you've written it, then it is incorrect...and perhaps that's what you should say (rather than second-guess and try to reinterpret the question so as to make it correct) .

 

[HallsofIvy]

If a< b, c< d and either b and c are positive or a and d are positive then ac< bd.

From a< b and c positive you get ac< bc. from c< d and b positive what do you get? Can you combine them?