# How To Do: Proofs By Deduction

**Why Are We Here?**

Because AS Maths shouldn’t be that hard. Life would be easier if you could condense a week’s worth of teaching into a 5 minute blog post wouldn’t it? Well we can. And we’re starting with “Proofs” – specifically “Proofs by Deduction”…

**Definition:**

A deductive proof is a logical argument that uses known facts and logical inferences to prove a theorem is true.

**When Writing a Proof You Should Always:**

- State all the known facts and theorems that you’re using
- Write out every step clearly, ensuring that each one follows logically from the step before
- Finish the proof by stating what you’ve proved

### Example 1:

**Tip:**

You will often be asked to prove identities. To do this, look at the expression on one side of the identity and manipulate it algebraically until it looks like the other side.

### Example 2:

**Conclusion:**

Well there you have it, a five-minute guide to “Proofs By Deduction”. Stay tuned for more AS Maths guides…

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