Math (Midterm) Modules 1-3 Questions With Complete
Solutions
(Confess, Confess) Correct Answer Which of the following is
the maximin solution of the Prisoner's Dilemma game?
(Stag, Stag) and (Rabbit, Rabbit) Correct Answer Two hunters
have set off the get food from the forest, They have two possible
games that they can hunt: either a stag or rabbits. If both players
hunt the stag, then they succeed in bringing it down; this gives
them both a payoff of 2 units of food. If one player hunts the
stag and the other hunts rabbits, then the stag hunter will fail
while the rabbit hunter will succeed; i.e. the stag hunter hunter
gets a payoff of 0 while the rabbit hunter gets a payoff of 1.
Finally, if both hunters pursue rabbits, they both receive a payoff
of 1. The payoff matrix for this game is shown below.
Determine all the Nash equilibria of the game (if there are any).
(X,A) and (X,C) Correct Answer Consider the normal form of
the game with two players. What is the Nash equilibrium of the
game?
¬ p ∨ q Correct Answer Suppose p is the proposition "4 is a
perfect square" and q is the proposition "5 is an odd number."
Which of the following is the symbolic representation of the
statement"4 is not a perfect square or 5 is an odd number?"
¬ r ⇒ ¬ ( p ∧ q ) Correct Answer When p and q are both true
propositions while r is false, which of the following has truth
value of false?
,∧ Correct Answer Which of the following is the symbol for a
conjunction?
∴ p ⇒ r Correct Answer Hypothetical Syllogism
p⇒q
q⇒r
∴ㄱ P Correct Answer Modus Tollens
ㄱQ
P
⇒Q
1750.60% Correct Answer On July 5, 1994, SM Prime
Holdings, Inc. (SMPH) has its IPO at P2.0669 per share. On
July 5, 2019, the market value of SMPH was P38.25.
Disregarding dividends, what is the ROI of an SMPH stock held
for those 25 years?
190,000 Correct Answer How much income tax is due from a
resident citizen with a taxable income of Php1,000,000 in 2018
2.92% Correct Answer Jam invested P500,000 in BPI
Philippine Equity Index Fund on Aug 6, 2019 at a NAVPU of
P104.75. On Sep 13, the NAVPU was P107.81. What is the
absolute ROI if redemption was made on Sep 13, 2019? Assume
that the fund has neither front nor back load.
2nd player Correct Answer In a game called NIM, there are
two players. At the start, two piles of matches are placed on the
table in front of them, each containing two matches. In turn, the
, players take any (positive) number of matches from one of the
piles. The player taking the last match loses. Which player is
sure to win in this game?
4,773.2697 units Correct Answer Jam invested P500,000 in
BPI Philippine Equity Index Fund on Aug 6, 2019 at a NAVPU
of P104.75. Assume that the fund has neither front nor back
load. How many units was Jam able to purchase?
45 30 25
ABC
CAB
B C A Correct Answer The Mathematics Society is holding an
election for the president. The three candidates are A, B, C.
45% of voters like A the most and B the least. 30% of voters
like B the most and C the least. 25% of voters like C the most
and A the least. Write out the preference schedule for this
election.
5.71% Correct Answer A bond with face value P10,000 has a
semiannual rate of 6%. With a time to maturity of 3 years, the
bond is sold for P10,500. What is the current yield of the buyer?
8 Correct Answer Suppose there are 3 propositions in a
compound statement (for example, P ∨ ( Q ∧ ¬ R )) and you
want to construct a truth table for this. How many combinations
of truth values will there be in this table?
88 Correct Answer Given the following preference table, the
Borda score of Candidate S is ______
Solutions
(Confess, Confess) Correct Answer Which of the following is
the maximin solution of the Prisoner's Dilemma game?
(Stag, Stag) and (Rabbit, Rabbit) Correct Answer Two hunters
have set off the get food from the forest, They have two possible
games that they can hunt: either a stag or rabbits. If both players
hunt the stag, then they succeed in bringing it down; this gives
them both a payoff of 2 units of food. If one player hunts the
stag and the other hunts rabbits, then the stag hunter will fail
while the rabbit hunter will succeed; i.e. the stag hunter hunter
gets a payoff of 0 while the rabbit hunter gets a payoff of 1.
Finally, if both hunters pursue rabbits, they both receive a payoff
of 1. The payoff matrix for this game is shown below.
Determine all the Nash equilibria of the game (if there are any).
(X,A) and (X,C) Correct Answer Consider the normal form of
the game with two players. What is the Nash equilibrium of the
game?
¬ p ∨ q Correct Answer Suppose p is the proposition "4 is a
perfect square" and q is the proposition "5 is an odd number."
Which of the following is the symbolic representation of the
statement"4 is not a perfect square or 5 is an odd number?"
¬ r ⇒ ¬ ( p ∧ q ) Correct Answer When p and q are both true
propositions while r is false, which of the following has truth
value of false?
,∧ Correct Answer Which of the following is the symbol for a
conjunction?
∴ p ⇒ r Correct Answer Hypothetical Syllogism
p⇒q
q⇒r
∴ㄱ P Correct Answer Modus Tollens
ㄱQ
P
⇒Q
1750.60% Correct Answer On July 5, 1994, SM Prime
Holdings, Inc. (SMPH) has its IPO at P2.0669 per share. On
July 5, 2019, the market value of SMPH was P38.25.
Disregarding dividends, what is the ROI of an SMPH stock held
for those 25 years?
190,000 Correct Answer How much income tax is due from a
resident citizen with a taxable income of Php1,000,000 in 2018
2.92% Correct Answer Jam invested P500,000 in BPI
Philippine Equity Index Fund on Aug 6, 2019 at a NAVPU of
P104.75. On Sep 13, the NAVPU was P107.81. What is the
absolute ROI if redemption was made on Sep 13, 2019? Assume
that the fund has neither front nor back load.
2nd player Correct Answer In a game called NIM, there are
two players. At the start, two piles of matches are placed on the
table in front of them, each containing two matches. In turn, the
, players take any (positive) number of matches from one of the
piles. The player taking the last match loses. Which player is
sure to win in this game?
4,773.2697 units Correct Answer Jam invested P500,000 in
BPI Philippine Equity Index Fund on Aug 6, 2019 at a NAVPU
of P104.75. Assume that the fund has neither front nor back
load. How many units was Jam able to purchase?
45 30 25
ABC
CAB
B C A Correct Answer The Mathematics Society is holding an
election for the president. The three candidates are A, B, C.
45% of voters like A the most and B the least. 30% of voters
like B the most and C the least. 25% of voters like C the most
and A the least. Write out the preference schedule for this
election.
5.71% Correct Answer A bond with face value P10,000 has a
semiannual rate of 6%. With a time to maturity of 3 years, the
bond is sold for P10,500. What is the current yield of the buyer?
8 Correct Answer Suppose there are 3 propositions in a
compound statement (for example, P ∨ ( Q ∧ ¬ R )) and you
want to construct a truth table for this. How many combinations
of truth values will there be in this table?
88 Correct Answer Given the following preference table, the
Borda score of Candidate S is ______
