Answer to Question #291791 in Discrete Mathematics for favor

Question #291791

Symbolic Logic

Can you figure out the values of the following below? Why or why not

1.    (H ≡≡ A) ⊃J (G ≡≡ B)

2.    ~ (X· G)

For each of the following pairs of sentences below, indicate whether (1) is a sufficient condi[1]tion for (2), a necessary condition for (2), both, or neither

3.   (I) Amy is not a student. (2) Amy is neither a student nor a teacher.

4.   (1) John loves Mary. (2) Someone loves Mary.



1
Expert's answer
2022-02-01T17:21:59-0500

1. We cannot figure out since the truth values of all components are unknown so we cannot deduce a relation

2. We cannot figure out since the truth values of both components are unknown

3. It is neither a sufficient condition nor a necessary condition. This is so because the non-existence of condition (1) does not guarantee the non-existence of condition (2) hence it is not a necessary condition and also the existence of condition (1) does not guarantee the truth of condition (2) hence it is not a sufficient condition

4. It is a sufficient condition since the existence of condition (1) guarantees the truth of condition (2).


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