Mathematics
Suppose a + b = c + d, and a < c. Use proof by contradiction to show b > d.
Mathematics Proofs
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Answer
Suppose b ≤ d,
Given,
⇒ a + b = c + d
⇒ c - a = b - d ………..(1)
Since, a < c so, c - a will be positive.
According to equation (1),
b - d = c - a
∴ b - d will also be positive.
It is not possible as we have assumed b ≤ d.
So, our assumption is wrong.
Hence, proved that b > d.
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