and labeled on separate paper.
use explicit words like “NOT”, “OR”, “COMPLEMENT”, “UNION”, etc. instead of special characters.
from elsewhere, will be marked a zero. If this recurs, the entire assignment will be marked a zero.
Problem 1 (28 pts)
All the following statements are false or incorrect. Explain why. Provide a direct counterexample or a simple Venn diagram, if necessary, to make your point.
1A + 2B = 46
She doesn’t like my lasagna when I put sausages in it. She didn’t like my
lasagna yesterday. So I must have put sausages in it.”
pizzas with no toppings), then it offers a total of exactly 25 pizzas with at least 2 toppings.
Problem 2 (6 pts)
Let N be the set of distinct letters in the word “Nassau” and S be the set of distinct letters in
the word “Suffolk.”
a. Find the set (N ∪ S) − (N ∩ S).
b. List all the subsets of N.
Problem 3 (6 pts)
Consider the following conditional statement: “Peanuts are neither peas nor nuts.”
a) Write the contrapositive of this statement.
b) Write the negation of this statement.
Problem 4 (8 pts)
A recent culinary survey asked 50 chefs on Long Island whether they are currently cooking French
and/or Italian dishes at their restaurants. Here are the results of that survey:
• 16 chefs said they feature French dishes on their menus.
• 22 chefs said they feature Italian dishes on their menus.
• 21 chefs said they feature neither French nor Italian dishes on their menus.
Draw a Venn diagram for this survey below.
a. How many chefs feature only French dishes on their menus? __
b. How many chefs feature both Italian and French dishes on their menu? __
c. How many chefs do not feature Italian dishes on their menu? ______
Problem 5 (4 pts)
Show that the statement (p ∧ q) → (p ∨ q) is a tautology without using a truth table.
Problem 6 (10 pts)
Your friend tells you the following:
“If I get a puppy this summer, then my sister will not come to my pool party. My sister
will come to my pool party or my mother will be upset. I ultimately decided not to get a
puppy this summer. So now I know my mother won’t be upset!”
a. Show your friend’s argument in symbolic form using three basic statements p, q and r. Write
out these components explicitly.
b. Analyze the argument by any means (truth values, truth table, standard forms). Is your friend’s
logic valid or not
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