I have started a new chapter and I do not quite understand how you start questions like these? Do i need to just keep doing contradictions to get an answer like this? Can someone point me in the right direction or help me? Premise: B ↔ ￢B Conclusion: J ↔ ￢C
closed as off-topic by Conifold, Jishin Noben, Alexander Gegg, Eliran, YiFan Apr 27 at 11:46
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One way to start the problem is to put the premise and conclusion in a proof checker and then use the inference rules programmed into the proof checker to reach the conclusion. For this problem since the premises lead to a contradiction whether you start with "B" or "¬B", you can use the law of the excluded middle to reach any result.
Here is how I did it using the proof checker linked to below with a text book explaining the rules in more detail.
To use the law of the excluded middle I considered both case "B" on lines 2-5 and case "¬B" on lines 6-9. I reached the same conclusion using explosion (X) on lines 5 and 9 and finished by invoking the law of the excluded middle (LEM) on line 10.
This may not match what you need to do but hopefully it provides a hint how you might proceed.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/