This is discrete Structures math help please thank you!! Example 1.3.1: Automati

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This is discrete Structures math help please thank you!!

Example 1.3.1: Automatic degree requirements check.

Large universities with thousands of students usually have an automated system for checking whether a student has satisfied the requirements for a particular degree before graduation. Degree requirements can be expressed in the language of logic so that they can be checked by a computer program. For example, let X be the proposition that the student has taken course X. For a degree in Computer Science, a student must take one of three project courses, P1, P2, or P3. The student must also take one of two theory courses, T1 or T2. Furthermore, if the student is an honors student, he or she must take the honors seminar S. Let H be the proposition indicating whether the student is an honors student. We can express these requirements with the following proposition:

(P1 P2 P3 ) (T1 T2) (H S)

Additional exercises

Exercise

1.3.1: Truth values for conditional statements in English.

Which of the following conditional statements are true and why?

If February has 30 days, then 7 is an odd number.

True. The hypothesis is false and the conclusion is true.

If January has 31 days, then 7 is an even number.

If 7 is an odd number, then February does not have 30 days.

If 7 is an even number, then January has exactly 28 days

question 2))

1.3.2: The inverse, converse, and contrapositive of conditional sentences in English.

Give the inverse, converse and contrapositive for each of the following statements:

If she finished her homework, then she went to the party.

Inverse: If she did not finish her homework, then she did not go to the party.

Contrapositive: If she did not go to the party, then she did not finish her homework.

Converse: If she went to the party, then she finished her homework.

If he trained for the race, then he finished the race.

If the patient took the medicine, then she had side effects.

question 3

1.3.3: Expressing conditional statements in English using logic.

Define the following propositions:

c: I will return to college.

j: I will get a job.

Translate the following English sentences into logical expressions using the definitions above:

Not getting a job is a sufficient condition for me to return to college.

¬j c

If I return to college, then I won't get a job.

I am not getting a job, but I am still not returning to college.

I will return to college only if I won't get a job.

There's no way I am returning to college.

I will get a job and return to college.

(P1 P2 P3 ) (T1 T2) (H S)

Explanation / Answer

Since 1 Qn per post is allowed, you may post the 1.3.2 nd and onwards separately to get answer to the same.

For a degree in Computer Science, a student must take one of three project courses, P1, P2, or P3. Hence, this is going to be a "OR" connector.

The student must also take one of two theory courses, T1 or T2.

Again, an "OR" connector.

Furthermore, if the student is an honors student, he or she must take the honors seminar S. Let H be the proposition indicating whether the student is an honors student.

H implies S, So H-->S

The above condition overlays on Px and Tx choices. Hence, a intersection will come into the picture

This is right:

(P1 P2 P3 ) (T1 T2) (H S)

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This is discrete Structures math help please thank you!! Example 1.3.1: Automati

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