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CORE 1 proof

CORE 1 proof. What is Mathematical Proof?. The process of starting with an assumption, or a statement which is given, and, by using logical argument, arriving at a conclusion. Mathematical Proof. ‘Prove that …’ or ‘Given …, prove …’ or ‘ Prove …, given …’ Form a logical argument

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CORE 1 proof

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  1. CORE 1proof

  2. What is Mathematical Proof? The process of starting with an assumption, or a statement which is given, and, by using logical argument, arriving at a conclusion

  3. Mathematical Proof ‘Prove that …’ or ‘Given …, prove …’ or ‘ Prove …, given …’ Form a logical argument Start with what is given or standard results Deduce each step from previous Standard results can be used at any stage

  4. MATHEMATICAL STATEMENTS ΔABC is isosceles sinθ = ¾ The gradient of y=mx+c is m

  5. Implication Signs Use to express the relationship between statements implies does not imply is implied by implies and is implied by

  6. Example: A Prove that ΔABC is isosceles AB = AC ‗B = _C AB = AC ΔABC is isosceles B C

  7. Example: Link the statements a = 0 and ab = 0 using implication signs. a = 0 ab = 0 ab = 0 a = 0 (b could be 0) ab = 0 Either a = 0 or b = 0

  8. Example:

  9. Example: Prove that sum of an even number and an odd number is always odd.

  10. Let 2n be any even number, where n is an integer. 2m + 1 be any odd number, where m is an integer. 2n + 2m + 1 = 2(n+m) + 1 n+m is an integer n+m is an integer 2(n+m) is even 2(n+m) + 1 is odd 2(n+m) + 1 = 2n + 2m + 1 the sum of an even number and an odd number is always odd.

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