Discrete Mathematics Answers

Let p, q, and r be the propositions

p: You have the flu.

q: You miss the final examination.

r: You pass the course.

Express each of these propositions as an English sentence.

p → q

Show, by the use of replacement rules, that (-p ^ q) ^ (q→p) = F

 are logically equivalent.

Show, by the use of the truth table (truth matrix), that the is a contradiction.

                                       ( pvq ) へ [ ( -p ) へ ( -q ) ]

Show that  -p > (q → r) and q → (p V r) are logically equivalent.

Symbolize the following by using qualifiers, predicates and logical connectives.

1. All rational numbers are real numbers.
2. some rational numbers are integers.
3. some even numbers are multiplied of two four and five.
4. some triangles are scalene.
5. every integer is multiple of 10 if and only if it is a mulple of 5 and 2.

D. Write in the form " if p then q", then write converse, inverse and contra positive of each of the following implications.

1. it is necessary to do your homework to get a passing grade.
2. if you read your lesson everyday, you will pass all your courses.

write the negation of these propositions

1. Today is Monday
2. The air in Naic Cavite is hot and polluted.
3. Summer in Davao is hot and sunny.
4. 2 + 1 > 5
5. it is hot.
6. X + y = 4
7. 7. sierra madre mountains are denuded.
8. a x b > 6
9. it's raining in August.
10. it is cold in December

•Construct the truth table of the converse,

contrapositive, and inverse of p→ q

•Let p, q, and r be propositions. Construct the

truth table of r→(˥p⋀q)

1.    Show that are logically equivalent. P ↔ Q and (P ∧ Q) V ( ¬P ∧ ¬Q)

 Your answer sheets showing your name and solution.

1. Given the following:

·        g: "You can graduate."

·        m: "You owe money to the college."

·        r: "You have completed the requirements of your major."

·        b: "You have an overdue book."

Translate "You can graduate only if you have completed the requirements of your major, you do not owe money to the college, and you do not have an overdue book." into a propositional logic.

2. Show that  are logically equivalent.

3. Show, by the use of the truth table (truth matrix), that the  is a contradiction.