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How do I prove that ac<bd?
How do I prove that ac<bd given the conditions that a,b,c,d are integers and 0<a<b and 0<c<d?
Has to use the Axioms for Integer, division is not allowed, only the basic operations of addition and multiplication.
3 Answers
- ?Lv 71 decade agoFavorite Answer
Since 0<a<b and c is positive, ac < bc
Since 0<c<d and b is positive, bc < bd
By the transitive property, ac < bc and bc < bd implies ac < bd
- δοτζοLv 71 decade ago
Given: 0 < a < b, 0 < c < d
Prove ac < bd
a / b < d / c
Since a < b, a / b < 1.
Since c < d, d / c > 1
Therefore
a / b < 1 < d / c
and so
ac < bd
■
Pretty simple algebraic proof.
