Deductive Reasoning, Part 1

Given the following true logical statement:

If inputs x1, x2, and x3 are all true, then output y is true.

1.       Write this statement as a logical statement using the appropriate logic symbols for conjunction and implication.

2.       Write the converse and contrapositive of this statement.

3.       Is the converse true? Explain why or why not.

4.       Is the contrapositive true? Explain why or why not.

 

Deductive Reasoning, Part 2

Assume you are a systems manager and that you know a server will log an error message if a database has a retrieval error. With that, complete the following:

1.       Why is it important for errors to be logged?

2.       What is a database retrieval error, and what might cause this type of error?

3.       If you notice that there is an error logged, can you infer that a retrieval error has occurred without reading the log? Explain why or why not. (Hint: This is a question about reasoning.)

 

 

Please write out fully and solve following discrete math questions

 

In this Exercise show that A=B

A = {1, 2, 3}, B = {n |n ∈ Z+ and n2 < 10}

 

In this Exercise that A ⊆ B

A = {1, 2}, B = {x | x3 − 6x2 + 11x = 6}