Please Answer the following

Let p denote "I drive to the mall" and q denote "I am drunk." Which of the following represents the compound proposition "I will drive to the mall if and only if I am not drunk"?

Question 1 options:

a)

q > ~p

b)

~p q

c)

p < ~q

d)

p > q

Which of the following is not correct?

Question 2 options:

a)

p ^ q = q ^ p

b)

~(~p) = p

c)

~p v ~q = ~( q ^ p)

d)

~p v q = p v ~q

Let p denote "I bought a lottery ticket this week" and q denote "I won the million-dollar jackpot on Friday." Which of the following is a contradiction?

Question 3 options:

a)

I bought a lottery ticket this week and I did not win the million-dollar jackpot on Friday.

b)

I did not win the million-dollar jackpot this on Friday and I won the million-dollar jackpot on Friday.

c)

I did not buy a lottery ticket this week but I won the million-dollar jackpot on Friday.

d)

I did not buy a lottery ticket this week or I bought a lottery ticket this week

Let p and q be the propositions "Swimming at the New Jersey shore is allowed" and "Sharks have been spotted near the shore," respectively. Which of the following is the correct form as an English sentence for ~p v (p ^ ~q)?

Question 4 options:

a)

Swimming at the New Jersey shore is allowed, and Sharks have not been spotted near the shore.

b)

Swimming at the New Jersey shore is not allowed or swimming at the New Jersey shore is allowed when sharks have not been spotted near the shore.

c)

Swimming at the New Jersey shore is not allowed or swimming at the New Jersey shore is not allowed when sharks have been spotted near the shore.

d)

Swimming at the New Jersey shore is not allowed, and sharks have not been spotted near the shore.

Question 5 (2 points)

Which of the following is a contradiction if q denotes "She likes to drink low-fat milk"?

Question 5 options:

a)

~( q ^ ~q)

b)

~(~q ^ q)

c)

q v ~q

d)

q ^ ~q

Which sentence below is not a proposition?

Question 6 options:

a)

I am not a high school student now.

b)

The moon is full of vegetables.

c)

2 + 3 = 6.

d)

What time is it now?

Which of the following is equivalent to p v q?

Question 7 options:

a)

~( p q)

b)

~p ^ ~q

c)

~( ~(p v q)

d)

~(~p) ^ ~(~q)

Which sentence below is not a TRUE proposition?

Question 8 options:

a)

Do not close the door!

b)

I am a Trident student now.

c)

x + 2 = 11

d)

Washington D.C. is the capital of the United States.

e)

2 + 3 = 6

Let p and q be the propositions p: "I bought a lottery ticket this week" and q: "I won the million-dollar jackpot." Which English sentence express the proposition ~p ~q?

Question 9 options:

a)

If I bought a lottery ticket this week then I did not win the million-dollar jackpot.

b)

If I did not buy a lottery ticket this week then I did not win the million-dollar jackpot.

c)

If I bought a lottery ticket this week then I won the million-dollar jackpot.

d)

If I did not buy a lottery ticket this week then I won the million-dollar jackpot.

Which is the negation for the statement "Dave is 6 feet tall, and he weighs 200 pounds"?

Question 10 options:

a)

Dave is 6 feet tall but he does not weigh 200 pounds.

b)

Dave is not 6 feet tall or he weighs 200 pounds.

c)

Dave is not 6 feet tall and he does not weigh at least 200 pounds.

d)

Dave is not 6 feet tall or he does not weigh 200 pounds.

From following truth table:

p

q

~p

~pq

pq

T

T

F

T

T

T

F

F

F

F

F

T

T

T

T

F

F

T

T

T

Which conclusion can be drawn:

Question 11 options:

a)

p and ~p are equivalent.

b)

~p v q and pq are equivalent.

c)

p and q are equivalent.

d)

q and ~p v q are equivalent.

Let p and q be the propositions "Swimming at the New Jersey shore is allowed" and "Sharks have been spotted near the shore," respectively. Which of the following is a tautology?

Question 12 options:

a)

Swimming at the New Jersey shore is not allowed, and swimming at the New Jersey shore is allowed.

b)

Swimming at the New Jersey shore is not allowed or swimming at the New Jersey shore is allowed.

c)

Sharks have been spotted near the shore and swimming at the New Jersey shore is not allowed.

d)

Sharks have not been spotted near the shore and swimming at the New Jersey shore is allowed.

Which sentence below is not a FALSE proposition?

Question 13 options:

a)

2 + 3 = 6

b)

I am not a Trident student now.

c)

Washington D.C. is the capital of the United States.

d)

x + 2 = 11

Which of the following sentences is a proposition with truth value of TRUE?

Question 14 options:

a)

Give me your ticket.

b)

Miami is the capital of Florida.

c)

All odd numbers are dividable by 2.

d)

2 + 3 = 5.

Let p denote "It is not cold." Let q denote "I like to drink hot cocoa."Which of following represents the sentence, "If it is cold, then I like to drink hot cocoa"?

Question 15 options:

a)

~p <-> q

b)

~pq

c)

~p~q

d)

p~q