1) A statement/proposition is a sentence that is either true or false. Which of the following are (valid) statements?

a) Will this class be fun?

b) Next year the stock market will go up.

c) Three is a prime number.

d) Five is an even number.

e) She is shorter than 60 inches.

2) "A or B" questions:

If A is true and B is true, what truth value would you assign to A B?

If A is true and B is false, what truth value would you assign to A B?

If A is false and B is true, what truth value would you assign to A B?

If A is false and B is false, what truth value would you assign to A B?

3) "A implies B" Questions:

If A is true and B is true, what truth value would you assign to A B?

If A is true and B is false, what truth value would you assign to A B?

If A is false and B is true, what truth value would you assign to A B?

If A is false and B is false, what truth value would you assign to A B?

4) More "A implies B" Questions:

If A B is true and A is true, what truth value must B have?

(Therefore, we say "A is a for B")

If A B is true and B is false, what truth value must A have?

(Therefore, we say "B is for A")

5) Complete the following truth tables.

    "conjunction" "disjunction" "implication" "equivalence"
    "A and B" "A or B" "A implies B" "A is equivalent to B"
A B A B A B A B A B
T T        
T F        
F T        
F F        
Alternative

Phrases

"A also B"

"A, but B"

"A. In addition B"

"A inclusive or B" "If A, then B"

"B follows from A"

"A is a sufficient

condition for B"

"B is a necessary condition for A"

"A only if B"

"A if and only if B"

"A iff B"

"A is necessary and sufficient for B"

           
Operand Names "conjuncts" "disjuncts" "antecedent"

"consequent"

 
6) Consider the following implication: "If it is snowing on Friday, then I will go for a walk on Friday." If it is not snowing on Friday and I go for a walk, is the statement still true?

7) For the following implication: "If it is snowing on Friday, then I will go for a walk on Friday."

a) What is the antecedent?

b) What is the consequent?

c) Reword the statement in the form "A is a sufficient condition for B."

d) Reword the statement in the form "B is a necessary condition for A."

8) Use a truth table to show that A B is equivalent to A (B').

A B A B B' A (B')
T T      
T F      
F T      
F F