Discrete Mathematics Answers

How many rows appear in a truth table for each of these compound propositions?

a) p → ¬p

b) (p ∨ ¬r) ∧ (q ∨ ¬s)

c) q ∨ p ∨ ¬s ∨ ¬r ∨ ¬t ∨ u

1. Determine whether the following is a set or not a set.

a. The list of course offering of UPHR-Molino Campus. -SET

b. The elected barangay officials of Bacoor City. -SET

c. The collection of intelligent students of College Department. -NOT A SET

2. List the elements of the following sets.

a. A = {x/x is a letter in the word mathematics}

b. B = {x/x is a positive integer, 3 ≤ x ≤ 8}

c. C = {x/x = 2n + 3, n is a positive integer}

3. Given U = {x/x is the set of letters in the English alphabet;

A = {a, e, i, o, u ,

B = {x/x is the set of consonant letters} ; and

C = { a, b, c, d, e}.

Tell whether the statement is true or false.

a. B ⊂ U

b. C ⊂ B

c. A ⊆ B

d. B = A

4. Determine the cardinal number sets in given No. 3 such as

a. universal set (U)

b. set A

c. set B

d. set C

R₃ = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),

(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

1. Determine whether the relation R₃ is reflexive, symmetric, anti-symmetric and transitive.    
2.  Determine whether the relation R₃ is an equivalence relation or partial order. Give reason for your answer                                    

ASAP

Determine all the winning coalitions and find the Banzhaf power distribution

[16:5,5,11,6,3]

SHOW ALL WORK