Discrete Mathematics Answers

Convert the following formula to conjunctive normal form: A ⇒ ( B ∧ C )

A. ( ¬A ∨ B ) ∧ ( ¬A ∨ C )

B. ( A ∧ ¬B ) ∨ ( A ∧ ¬C )

C. ( ¬A ∧ B ) ∨ ( ¬A ∧ C )

D. ( A ∨ ¬B ) ∧ ( A ∨

The population of City A is 8,000,000 at the end of the year 2020.The

number of immigrants is 25,000n at the end of year n. The population

of city increases at the rate of 8% per year. Use recurrence relation to

determine the population of the city at the end of 2030.

Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.

Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter Y in the

set of all months of the year.

show that p ↔ q and (p^q) v (¬p ^ ¬q) are logically equivalent.

Use a Venn diagram to illustrate the subset of even integers in the set of all positive integers not exceeding 15. 

Let R1 and R2 be two relation on real number such that R1 = {(x, y)|x < y} and R2 =

{(x, y)|x > y}, then find R1 ∪ R2,R1 ∩ R2,R1 − R2, R2 − R1, and R1

LR2.

Give an example of relation which is Reflexive, anti symmetric & transitive but not symmetric

Show that p > q and (p A q) V (-p ^ ¬q are logically equivalent.

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!