Search & Filtering
- What is the cardinality of each of these sets?
- Æ
- {Æ}
- {Æ,{Æ}}
- {Æ,{Æ},{Æ,{Æ}}}
A. Let A = {1,2,3,4,5,6,7,8}, B = [x∈ Z / x is divisible by 3} and C = {x∈ R | x2= 4v X3 = -1}. mark the following true or false.
- 2 ∈ A
- -2 ∈ A
- - 3 ∋ B
- 11 ∈ B
- 1 ∈ C
- 8 ∈ A ∪ B
- 8 ∈ A ∩ B
- 2 ∈ A ∩ C
- 5 ∈ A ∪ C
- 7 ∋ A ∪ B
B. Let ∪={1,2,3,4,5,6,7,8,9,10}, A={1,2,3,4,5,6,}, B={1,2,3,4,5,7}, C={,2,4,6,8,10}
- A ∩ B
- A ∪ C
- A ∩ B'
- A-C
- A' ∩ B'
- B-C
C. Let U={a,b,c,d,e,f,g,h,i}, A={a,b,c,d,e}, B= {d,e,f,g,h}
- A' ∩ B
- A ∩ B'
- (A ∩ B)'
- A-B
- A' ∩ B'
- (A∩ B)'
let P(x) be the statement "x has develop a program in JAVA", where the domain for x consist of all students. write a statement in english corresponding to the for
- ?x P(x)
- ?x ~p(x)
- ?x p(x)
- ~?x p(x)
- ~? ?x p(x)
List the members of these sets.
a) {x | x is a real number such that x 2 = 1}
b) {x | x is a positive integer less than 12}
Show that each of these conditional statements is a tautology
by using truth tables.
a) [¬p ∧ (p ∨ q)] → q
b) [(p → q) ∧ (q → r)] → (p → r)
c) [p ∧ (p → q)] → q
d) [(p ∨ q) ∧ (p → r) ∧ (q → r)] → r
Show that ¬p→(q→r) and q→(p ∨ r) are logically equivalent
Make a venn diagram Suppose that 53 of the 55 Information Technology students of University of Northern Philippines are taking atleast one of the mathematics subjects Mathematics in the Modern World, Discrete Mathematics, and Data management. Also suppose that: 24 taking Mathematics in the Modern World, 26 taking Discrete Mathematics, and 20 taking Data Management, 5 taking Mathematics in the Modern World and Discrete Mathematics, 7 taking Mathematics in the Modern World and Data Management, 8 taking Discrete Mathematics and Data Management.
- Let p and q be the propositions. (50 points)
p: It is below freezing.
q: It is snowing.
Express each of these propositions in complete English sentences.
a) p ∧ q (7 points)
b) p ∧ ¬q (7 points)
c) ¬p ∧ ¬q (7 points)
d) q ∨ p (7 points)
e) p → q (7 points)
f) q ∧ ¬p (7 points)
g) q → p (8 points)
2. Solve the following. (50 points)
a) Construct a truth table. (10 points)
¬p ∧ ( p ↔ ¬q )
b) Construct a truth table. (10 points)
p → ( q ∧ r )
c) Construct a truth table. (10 points)
( p → q ) ∨ ( ¬p ↔ r )
d) Find out if the following is a tautology, contradiction, or contingency. (10 points)
( p ∨ q ) ∧ ( ¬p ∧ ¬q )
e) Find out if the following propositions have logical equivalence. (10 points)
( p ↔ q ) ≡ ( p → q ) ∧ ( q → p )
How many circular permutations are there given the numbers on the clock?
Let p and q be the propositions “You can take the flight” and “You buy a ticket,” respectively.
Express each of these compound propositions as an English sentence.
a) ¬p b) p∨q
c) ¬p∧q d) q → p e) ¬q →¬p
f) ¬p →¬ q g) p ↔ q h) ¬q ∨(¬p∧ q)
