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Find, showing all working, a formula for the n-th term tn of the sequence (tn) defined by
t1 = 5; tn = -7tn-1 /3, n >= 2.
III. Determine the truth value of each of these statements if the domain consists of all integers. State your reason. 1. ∀𝑥, (𝑥 2 > 𝑥) 2. ∃𝑦, (𝑦 < 𝑦 2 − 1) 3. ∀𝑦, (𝑦 2 ≠ 𝑦) 4. ∃𝑥, 𝑦, (4𝑥 > 5𝑦) where 𝑥 < 𝑦 5. ∀𝑥, 𝑦, (𝑥𝑦 > 0) where 𝑥 = y
(4). Write the converse, inverse, and contrapositive of the statement “If
5 is an odd number, then it is a prime number.”
(5). Draw a truth table and determine for what truth values of p and q
the proposition ∼ q ∨ p is false.
(6). Construct truth tables for
(a) (∼ p ∨ q) =⇒ r
(b) p ∧ (q ∨ r) ⇐⇒ ∼ q
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)}
- Determine whether the relation R3 is reflexive, symmetric, anti-symmetric and transitive.
- 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
#339914 on Dec 2023