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Answer each question completely, including all lettered parts.
1. Which of these sentences are propositions? What are the
truth values of those that are propositions?
a) Miami is the capital of Florida.
b) 2 + 3 = 5.
c) 5 + 7 = 10.
d) x + 2 = 11.
e) Answer this question.
f) What time is it?
2. What is the negation of each of these propositions?
a) Mei has an MP3 player.
b) There is no pollution in New Jersey.
3. Let p and q be the propositions.
p: I bought a lottery ticket this week.
q: I won the million-dollar jackpot on Friday.
Express of each of these propositions as an English sentence:
a) ~p
b) p^q
c) p v q
d) (~p) ^ (~q)
4. Let p, q, and r be the propositions
p: You have the flu.
q: You miss the final 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
1. Which of these sentences are propositions? What are the
truth values of those that are propositions?
a) Miami is the capital of Florida.
b) 2 + 3 = 5.
c) 5 + 7 = 10.
d) x + 2 = 11.
e) Answer this question.
f) What time is it?
2. What is the negation of each of these propositions?
a) Mei has an MP3 player.
b) There is no pollution in New Jersey.
3. Let p and q be the propositions.
p: I bought a lottery ticket this week.
q: I won the million-dollar jackpot on Friday.
Express of each of these propositions as an English sentence:
a) ~p
b) p^q
c) p v q
d) (~p) ^ (~q)
4. Let p, q, and r be the propositions
p: You have the flu.
q: You miss the final 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
. Suppose that Peter visits the hostel mess sometime between 12:00 noon and 2:00 p.m.. He leaves the
mess after finishing his lunch in 20 minutes. Likewise, Gwen visits the same hostel mess sometime
between 1:00 p.m. and 2:00 p.m.. She also leaves the mess after finishing her lunch in 20 minutes. If the
probability of arrival of each person is uniform across the given intervals respectively, find the probability
that they meet in the mess.
mess after finishing his lunch in 20 minutes. Likewise, Gwen visits the same hostel mess sometime
between 1:00 p.m. and 2:00 p.m.. She also leaves the mess after finishing her lunch in 20 minutes. If the
probability of arrival of each person is uniform across the given intervals respectively, find the probability
that they meet in the mess.
the perimeter of a triangle is 45, if the largest side is twice the smallest and the medium side is the smallest increased by 5. find all three sides of the triangle.
Add using trigonometry (cosine and sine law) 7 m/s on a bearing of 030° and 2 m/s from a bearing of 343°.
UM=2x+14
MS=14+x
Find US
MS=14+x
Find US
UM=2x+14
MS=14+x
Find US
MS=14+x
Find US
A positive real number x lies between positive integers k and k+1 satisfying x.3^x = 3^18, then k =
Math
Q. Solve this degeneracy problem
11 〖2 〗^8 8 〖6 〗^6 〖2 〗^4 Supply
〖9 〗^10 9 12 9 6 18
7 6 〖3 〗^8 7 7 10
〖9 〗^2 3 5 〖6 〗^2 11 8
Demand 12 8 8 8 4 4
11 〖2 〗^8 8 〖6 〗^6 〖2 〗^4 Supply
〖9 〗^10 9 12 9 6 18
7 6 〖3 〗^8 7 7 10
〖9 〗^2 3 5 〖6 〗^2 11 8
Demand 12 8 8 8 4 4
Math
Q. Solve this degeneracy problem
Dealer 1 2 3 4 Supply
A 2 2 2 4 1000
B 4 6 4 3 700
C 3 2 1 0 900
Demand 900 800 500 400
Dealer 1 2 3 4 Supply
A 2 2 2 4 1000
B 4 6 4 3 700
C 3 2 1 0 900
Demand 900 800 500 400
Math
Q.Solve by NWCM (north-west corner method) and find optimal solution by UV method
3 1 7 4 Supply
2 6 5 9 250
8 3 3 2 350
Demand 200 300 350 400
3 1 7 4 Supply
2 6 5 9 250
8 3 3 2 350
Demand 200 300 350 400
