Discrete Mathematics Answers

Let X={1,2} and Y={a,b,c}. List the elements in each set.

(4). Construct a difference table to predict the next term of each sequence.

(a) 9, 4, 3, 12, 37, 84, ...

(b) 10, 10, 12, 16, 22, 30, ...

(7). Use Polya’s four-step problem-solving strategy and the problemsolving procedures to solve each of the following exercises.

(a) An android phone and a bluetooth speaker together cost Php6500.00

. The phone costs Php2000.00 more than the speaker.What is

the cost of the phone?

(b) In how many ways can you answer a 12-question true-false test

if you answer each question with either a “true” or a “false”?

Use algebra of sets to prove that,

 [(𝐵 − 𝐴)' ∩ 𝐴] − 𝐴' = 𝐴

Make a Fully truth table and identify if it is a tautology, contradiction, contingency.

¬(¬(P∧Q)↔(¬P)∨(¬Q))

Let p, q, and r be the propositions

p : You have Covid.

q : You miss the prelim examination.

r : You pass the course.

Express each of these propositions as an English sentence.

a) p → q b) ¬q ↔ r

c) q → ¬r d) p ∨ q ∨ r

e) (p → ¬r) ∨ (q → ¬r)

f ) (p ∧ q) ∨ (¬q ∧ r)

Let p and q be the propositions

Let p and q be the propositions