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Flip to reveal answersWhat does "show that" / "prove" require?
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All 11 Flashcards — Deductive proof
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Question
What does "show that" / "prove" require?
Answer
A chain of justified steps from what you know to the result. The marks are the reasons, not the final answer.
Question
The golden rule of "show that" questions?
Answer
Start from the given (or one side) and work toward the target. Never start from the answer and work backwards.
Question
Difference between = and ≡?
Answer
= (equation) is true for particular values you solve for; ≡ (identity) is true for ALL values.
Question
How do you write an even and an odd integer in algebra?
Answer
Even = 2k, odd = 2k + 1, where k is an integer.
Question
How do you represent consecutive integers?
Answer
n, n + 1, n + 2, … — start from n and add 1 each time.
Question
Prove the sum of two odd numbers is even.
Answer
(2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1), which is even. Use different letters a, b.
Question
How do you show a number is a multiple of k?
Answer
Manipulate it until you can take out a factor of k: write it as k × (an integer).
Question
Why is n(n − 1) always even?
Answer
It is a product of two consecutive integers, and one of any two consecutive integers is even.
Question
Why must you use different letters for two unknowns?
Answer
Reusing one letter (e.g. 2k + 1 twice) forces the two numbers to be equal, which breaks a general proof.
Question
How should a proof end?
Answer
Reach the target exactly, then conclude in words — "… = 2m, which is even, so …". That sentence is often the last mark.
Question
Sum of three consecutive integers is a multiple of what?
Answer
3: n + (n + 1) + (n + 2) = 3(n + 1).
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Full study notes for Deductive proof
Topic 1.6 hub
Proof
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