1. 1 Determine a counter example to show that the following statement is incorrect:

The product of any two three-digit numbers is a five-digit number.

1. 2.Five salespeople gather for a sales meeting. How many handshakes are needed for each person to have shaken everybody else’s hand exactly once?
2. 3.Express the following set in roster form:

The set of states in the United States that have a common border with the state of Washington.

1. 4.Express the set in set builder notation.

A = {1,2,3,4,5,6,7,8,9}

1. 5.The Fitzgeralds are installing an in-ground pool in their backyard. They can either install the base model offered by the pool company or add any of the following options: automatic pool cleaner, solar cover, waterfall, hot tub, fountain, slide, diving board. How many different variations of the pool are possible?
2. 6.Let

U = {1,2,3,4,5,6,7,8} A = {1,2,4,5,7}

B = {2,3,5,6}

Find (A ∪ B) ∩ (A ∪ B)′.

1.  7.Let

                                                                           A = {1,2,3},            B = {a,b}

Does A × B = B × A?

1.  8.Use a Venn diagram to determine whether the statement

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

is true or not, for all sets A, B and C.

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1.  9.When the Montesano family members discussed where their annual reunion should take place, they determined that of all the family members,
   • 8 would not go to a park.
   • 7 would not go to a beach.
   • 11 would not go to the family cottage.
   • 3 would go to neither a park nor a beach.
   • 4 would go to neither a beach nor the family cottage.
   • 6 would go to neither a park nor the family cottage.
   • 2 would not go to a park or a beach or to the family cottage.
   • 1 would go to all three places.

What is the total number of family members?

1.  10.Construct a truth table for the statement

(p∨∼ q) ∧ r

1.  11.Determine the truth value of the statement (∼ r∧∼ q) ∧ (∼ r∨∼ p) if
   1. p is true, q is false, and r is true.
   2. p is false, q is true, and r is true.