proof by contradiction help

a,b,c,d are real positive numbers.

if ab=cd and a<=c and b<=d then a = c and b=d

how you show that by contradicition.

thanks.

You have to prove that ab = cd cannot possibly be true
If a <= c and b <= d is true
But one or both of a = c and b = d is false

Spoiler

EDIT: ignore this, I'm an idiot :P

how would you do that? im really confused.

See my spoiler thing above

We must have ab < cd (explain why)

how do you explain that. I get it part from how to explain that :smile:

cheers.

HamsterHam

We must have ab < cd (explain why)

how do you explain that. I get it part from how to explain that :smile:

cheers.

A is definately small than C so even if B and D are the same A multiplied by B will definitely be smaller than C multiplied by B

a is smaller than c
b is smaller than d

so how can the product of those 2 numbers possibly be equal to the product of cd?
obviously they can't.

Thankyou

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