Proof by Deduction (Edexcel A-Level Mathematics): Quizzes

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Proof by Deduction
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What is proof by deduction used for?

Deducing true statements from known truths

What does the symbol ⇒\Rightarrow mean in mathematical proof?

Implies that

Why is x2=9⇏x=3x^2 = 9 \not\Rightarrow x = 3 true?

Because xx could be ±3\pm 3

What does the symbol ⇔\Leftrightarrow mean?

If and only if

For P:x2+x−2=0P: x^2+x-2=0 and Q:x=1Q: x=1, what is the relationship?

P⇐QP \Leftarrow Q

What is the mathematical form of an even number?

2n2n where nn is an integer

What is the mathematical form of an odd number?

2n+12n+1 where nn is an integer

Why use different letters (e.g., 2n2n, 2m2m) for two even numbers in a proof?

The numbers may differ

Which form shows a number is odd?

2(n2+n)+12(n^2 + n) + 1

What does 2n+2m=2(n+m)2n + 2m = 2(n+m) prove?

Sum of two even numbers is even

Why is (2m+1)(2n+1)=2(2mn+n+m)+1(2m+1)(2n+1) = 2(2mn+n+m)+1 significant?

Proves product of two odds is odd

What does ⇐\Leftarrow mean in mathematical notation?

Right statement implies left

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