Logic question. I need help with indirect truth table Contradiction, I do not un

Question

Logic question.

I need help with indirect truth table Contradiction, I do not understand how to find out if something is a Contradiction using the indirect method

for example, this question, I know how to fill in the infomration but I am cunfuse as to why is it a Contradiction. Can you please explain

Also this one. I just dont underdstand how it is a Contradiction. please explain as simple as you can.

Thank you.

C D T T From the conclusion we can now derive the truth values of C and D, which are then transferred to the first two premises: F T F T T F F F The truth value of B is now derived from the second premise and transferred, together with the truth value of A, to the first premise: T T F F F F T F T T F F F A contradiction now appears in the truth values assigned to the first premise, since T F is F. The inconsistent truth values are circled. Because ever step was strictly necessitated by some prior step, we have shown that it is impossible for the premises to The argument is therefore valid.

Explanation / Answer

Well, while proving any conclusion using indirect truth table, we first assume all the premises operators are true (T) and the conclusion operator is false (F).

Now, a premise operator would be true iff Both Left hand sode and right hand side are ture (T)

But in your first example, in the circle you identified for the first premise Left hand side is T but right hand side is F

Hence it's a contradiction.

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