If I have A v B given in a logic proof is it legal to say A is true so that I can use it to conclude C is true from the statement if A then C.
I know that I can take A from A and B
to conclude C is true from if A then C.
But.. can I do the same thing with the or statement?
Yes, in a logic proof, if you have a statement A ∨ B and you want to conclude C based on the conditional statement if A then C, you can use the fact that A is true to establish C.
Here's how you can do it step by step:
1. Start with the premise A ∨ B.
2. Assume A is true and try to derive C.
3. Use the conditional statement if A then C.
4. From the assumption A, conclude C.
5. You have now established C based on the assumption that A is true.
Note that this approach is known as proof by cases or proof by disjunction. It allows you to consider different possibilities (either A is true or B is true) and analyze each case individually. By showing that C holds in one of the cases (when A is true), you can conclude that C holds overall.
So, yes, you can use the disjunction (or) statement to derive a conclusion using a conditional statement, just like you can with the conjunction (and) statement.