Search & Filtering
a) every student in this classes has taken exactly two mathematics classes at this school.
b) someone has visited every country in the world except Libya
Draw the Venn diagrams for each of these combinations
of the sets A, B, C, and D.
*A̅ ∪ B̅ ∪ C̅ ∪ D̅
Express the negations of each of these statements so that
all negation symbols immediately precede predicates.
∃x∃y(Q(x, y) ↔ Q(y, x))
let z be the set of integers and R be the relation on Z defined as: aRb if and only if 1+ab>0 then
1. Let p and q be the propositions “Swimming at the New Jersey shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence.
a) ¬q b) p ∧ q c) ¬p ∨ q d) p →¬q e) ¬q → p f ) ¬p →¬q
g) p ↔¬q h) ¬p ∧ (p∨ ¬q)
ACTIVITIES/ASSESSMENT:
A. Tell if the following statements are propositions or not.
1. Study hard!
2. The Apple Macintosh is a 16-bit computer.
3. 1 is an even number.
4. Why are we here?
5.8+7=13
B. p is "x < 50", q is "x > 40". Write the following in words.
1. ~P
2. ~q
3. p^ q
4. pv q 5. ~p ^ q
6. ~p~q
C. Construct a truth table for the following:.
1. PA (QVR) 2. (Ρ Λ Ω) v R
3. (PA~Q) V ~P 4. P→ (Q V~R)
5. [(PQ) v (P→ R)]
Given the following recurrence relation (M).
an = −4an−1 + 5an−2, a0 = 2, a1 = 8
The solution of (M) is:
a. an = 3 − (−5)
n
b. an = 3 + (5)
n
c. an = (3)
n − 5
d. None of these
