Mathematics
Prove that the sum of two odd numbers is even.
Mathematics Proofs
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Answer
Let x and y be two odd numbers.
Then x = 2k + 1 for some natural number and y = 2l + 1 for some natural number l.
Adding x and y, we get :
⇒ x + y = 2k + 1 + 2l + 1
= 2k + 2l + 2
= 2(k + l + 1).
We know that,
Any natural number on multiplying by 2 is an even number.
Hence, proved that the sum of two odd numbers is even.
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Related Questions
Find counter-examples to disprove the following statements:
(i) If the corresponding angles in two triangles are equal, then the triangles are congruent.
(ii) A quadrilateral with all sides equal is a square.
(iii) A quadrilateral with all angles equal is a square.
(iv) For integers a and b, = a + b
(v) 2n2 + 11 is a prime for all whole numbers n.
(vi) n2 – n + 41 is a prime for all positive integers n.
Take your favourite proof and analyse it step-by-step along the lines discussed in Section A1.5 (what is given, what has been proved, what theorems and axioms have been used, and so on).
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