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tdottoker
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Been at this all day and cannot come up with an instance where in english sentences, If P then Q is equivalent to It is not the case that P or Q. Can anyone provides some hints.. I am really stuck. Thanks!
tdottoker said:If P then Q is equivalent to It is not the case that P or Q.
To my mind, that doesn't clear up the ambiguity. You should follow the format for homework questions and state the (entire) problem. If you are asked to use English sentences for P and Q that have obvious truth values, I think the problem is to find particular instances of P and Q that make the two statements either both true or both false.tdottoker said:The question says it is an inclusive disjunction
tdottoker said:(a) Using a truth-table show that for arbitrary P and Q the above sentences
are logically inequivalent.
(b) In some special cases sentences of the above forms are logically equivalent. Give an example of this:.
tdottoker said:P: 2 + 2 = 4
Q: I am a pig
"If 2 + 2 = 4, then I am a pig".
Does this work?
tdottoker said:for b) it is only asking for the instance where both If P then Q and Not (Q or P) are false or a case when both are true (logically equivalent?)?
"If P then Q" is a logical statement that means if P is true, then Q must also be true. It is a way of expressing a cause and effect relationship between two statements.
"If P then Q" means that Q is true if and only if P is true. On the other hand, "Not the case that P or Q" means that both P and Q are not true at the same time. In other words, if P is false, then Q must also be false.
"If P then Q" is equivalent to "Not the case that P or Q" when P is false and Q is also false. This is because if P is false, then the statement "If P then Q" is automatically true, and the statement "Not the case that P or Q" is also true because both P and Q are false.
"If P then Q" and "Not the case that P or Q" are both logical statements that can be used to make predictions and draw conclusions in scientific research. They can help scientists determine cause and effect relationships and make hypotheses about the natural world.
No, "If P then Q" and "Not the case that P or Q" cannot both be true at the same time. This is because "If P then Q" states that if P is true, then Q must also be true, while "Not the case that P or Q" states that both P and Q cannot be true at the same time. Therefore, if one statement is true, the other must be false.