Symbolic logic problems

[mike1584]

Say that a sentence in our formal language is contingent if it is neither a tautology nor a contradiction. Let X and Y stand for sentences.

For each question below, if you answer “yes” provide a brief explanation; if you answer “no” provide a counterexample.

1) If X V Y is contingent, then either X is contingent or Y is contingent.
2) If X is contingent, then there is some contingent sentence Y such that X ^ Y is a contradiction.
3) If for all contingent sentences Y, X ^ Y is contingent, then X is a tautology.
4) If for some contingent sentence Y, X ^ Y is a contradiction, then X is contingent.

Thank you!

 

[Dr.Peterson]

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[pka]

Say that a sentence in our formal language is contingent if it is neither a tautology nor a contradiction. Let X and Y stand for sentences.
For each question below, if you answer “yes” provide a brief explanation; if you answer “no” provide a counterexample.
1) If X V Y is contingent, then either X is contingent or Y is contingent.
2) If X is contingent, then there is some contingent sentence Y such that X ^ Y is a contradiction.
3) If for all contingent sentences Y, X ^ Y is contingent, then X is a tautology.
4) If for some contingent sentence Y, X ^ Y is a contradiction, then X is contingent.

Mike, you can post your answer to one of the four so that we can see the level of your understanding.
We will note provide you with answers. That is your job with our help.