As the OP and the comments note, both of the results are tautologies.
Here is the truth table for the first one:
Here is the truth table for the second one:
As the OP notes the two sides of the biconditional are also tautologies.
As to why these were marked false, perhaps the answer key was in error or the problem that was intended was misstated. Perhaps ...
"A is B" and "A is not B"…. Are both of the above statements mutually
exclusive? If so, then would that not mean that the principle of
non-contradiction is self-evidently true?
Assume the truth of statements "A is B" and "A is not B". Now assume A is true. The combination of premises means that the following is true: B and not-B.
Such a conclusion is ...
There are two questions.
True or False? If monkeys can fly, then 1 + 1 = 3.
The antecedent of the conditional, "monkeys can fly" is false. So is the consequent, "1 + 1 = 3". In classical truth-functional logic the conditional connecting these two sentences also has a truth-value. Wikipedia describes this "material conditional" as follows:
The material ...
Let us first define lie, and determine what does and what does not count as a lie. In order for one to lie, one must report false data and they know that they are reporting false data.
One is not lying if one thinks that they are saying the truth.
I think that answers your question, A is lying if A is reporting false data and A knows that.
Which implies ...
This is an interesting question but there are, I think, a number of loose ends.
L1. Lying can be a matter of knowing something, typically a statement or set of statements, S1, to be false and intending by the actual use of some means of communication to deceive another person into believing that S1 is true.
This is not a definitive answer, but too long for a comment. The OP quote has a footnote listing the "proponents (and most opponents) of the knowledge argument" who take propositional knowledge "in a broader sense". Among the references are Lycan, who is classified by SEP under The New Knowledge/Old Fact View on Mary. According to this view, "what it is for ...
"S is P" ( S for subject, P for predicate) is analytic iff its negation is contradictory ( due to the fact that the concept of the predicate is contained, as says Kant, in the concept of the subject).
" Some bachelor is married" is clearly contradictory.
Is " Some apple is not a fruit" contradictory. Can we conceive of a possible world in which something ...
The usual term is an 'inconsistent triad' :
an inconsistent triad ... a collection of
propositions, any two of which are compatible with
each another but which, when viewed together in a
threesome, form a contradiction.
(Albert Weale, 'Rationing Health Care: A Logical Solution to an Inconsistent Triad', British Medical ...
You could rewrite "A or B" as "(A and not B) or (not A and B) or (A and B)".
You can see that these statements are equivalent using a truth table generator. Using the input
"((A&&~B)or(~A&&B)or(A&&B))<=>(A or B)" in this generator I find that all valuations of "A" and "B" give "T" values.
You could then decide with a separate if-...
Truth trees are a graphical device for a methodical search for counterexamples to a given set of premises. They are effective (for propositional logic) in the sense that the search either terminates with finding a counterexample, or with verifying that one does not exist by exhausting all options. They are more effective than truth tables because they ...
If A, consciously, reports false data to B, and B (or anyone else) has no way to verify, then no one can make the statement, "A lied". So, there exists no such person with respect to whom A lied.
Just because no one can verify something doesn't mean it didn't occur.
No one can verify your thoughts, so does that mean you never think?
If you know you lied, ...