Discrete Mathematics Answers

Use a short truth table to determine whether or not the following argument is valid.

R -> (M v ~C)

(P v U) -> C

M -> ~P

R -> U

Thus, (M & U) v ~R

Question 4 options:

Valid

Invalid when C is false, M is false.

Invalid when R is true, U is false.

Invalid when R is true, U is true.

Invalid when M is true, P is false.

Translate the following sentences and then use a short truth table to determine if the argument is valid.

If education was supported but taxes were not raised, then John was elected.

John was not elected although education was supported.

Taxes were raised only if John or Mary were elected.

So, neither education was supported nor Mary was not elected.

E = Education was supported.

J = John was elected.

M = Mary was elected.

R = Taxes were raised.

Question 5 options:

Valid

Invalid when R is true, M is true.

Invalid when R is false, M is true.

Invalid when E is true, R is false.

Invalid when R is true, M is false.

Translate the following argument and use a short truth table to determine whether or not the argument is valid.

Either scientists don't know what they are talking about, or the sun will eventually burn out and Earth will become dark and cold. If scientists don't know what they are talking about, then Mars is teeming with life. If Earth becomes dark and cold, then either the human race will migrate to other planets or will die out. Mars is not teeming with life, but the human race will not die out. Therefore, the human race will migrate to other planets.

S = Scientists know what they are talking about.

B = The sun will eventually burn out.

E = The Earth will become dark and cold.

M = Mars is teeming with life.

H = The human race will migrate to other planets.

D = The human race will die out.

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.

In a class of 16 students, there are 6 male students and 10 female students. In how many ways can you select a group of 5 students from this class such that 3 of the 5 students are males and the other two are females?

Solve

an+2 = 4an+1 + 21an; n  0 and a0 = 3; a1 = 4

1. Determine whether each of the following statements is a proposition or not. If it is, give its truth value.

• p: Mindanao is an island in the Philippines. 
• q: Find a number which divides your age. 
• r: My seatmate will get a perfect score in the Logic exam.
• s: Welcome to the Philippines!

1. Let p and q be propositions. p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives.

• You do not drive over 65 miles per hour.
• You will get a speeding ticket if you drive over 65 miles per hour.
• If you do not drive over 65 miles per hour, then you will not get a speeding ticket. 

1. Determine whether each of the following statements is a proposition or not. If it is, give its truth value.

• p: Mindanao is an island in the Philippines.

• q: Find a number which divides your age.

• r: My seatmate will get a perfect score in the Logic exam.

• s: Welcome to the Philippines!

 A f:X→Y where X,Y ∈ Z⁺ , and  0≤ X ≤23 and, 0≤Y≤59, X is hour of clock and Y is minute of digital clock, Proof the following

                                                       a.     Is f:X→Y is well defined

b.     Is f:X→Y a one-to-one correspondence 

 A f:X→Y where X,Y ∈ Z+ , and 0≥ X ≤23 and, 0≥ Y≤59, X is hour of clock and Y is minute of digital clock, Proof the following

a. Is f:X→Y is well defined?

b. Is f:X→Y a one-to-one correspondence