Aim: How do we solve truth tables?

Do Now: Complete the truth table.p q ~p ~q p ^ q p V q p q q p ~p ~q ~q ~p p q

• Negation (~) : makes the statement opposite of what it originally was (has the opposite truth value of the original statement.)

Ex: Original statement:

It is raining outside.

Negated Statement:

It is not raining outside

• Conjunction (^): connects two statements with “and”. For the conjunction to be true both statements must be true

Ex: The sun is not shining and it is raining outside

• Disjunction (V): connects two statements with “or”. For the disjunction to be true, at least one of the statements must be true.

Ex: The shoe is red or the shoe is blue

• Conditional ( ): connects two statements with “if…then”. For the conditional to be true, the “promise” must be kept.

Ex: If you do all your homework, then I’ll buy you ice cream.

• Biconditional ( ): connects two statements with “if and only if”. For the biconditional to be true, both statements have to be true or both have to be false.

Ex: I get paid a lot of money if, and only if I work all day

Inverse

Negates both the “if” and the “then” statements of a conditional

Converse

Switches the order of the “if” and “then” statements of a conditional.

Contrapositive

Negates and switches the order of the “if” and “then” statements of a conditional.

1) Which statement is logically equivalent to “If a triangle is an isosceles triangle, then it has two congruent sides”?

a) If a triangle does not have two congruent sides, then it is an isosceles triangle.

b) If a triangle does not have two congruent sides, then it is not an isosceles triangle

c) If a triangle is not an isosceles triangle, then it has two congruent sides.

d) If a triangle is an isosceles triangle, then it does not have two congruent sides.

2) What is the negation of the statement “The Sun is shining”?

(a) It is cloudy.

(b) It is daytime.

(c) The Sun is not shining.

(d) It is not raining.

3) The statement “If Joe does not start school in September, then he does not live in New York State” is the contrapositive to which of the following statements:

(a) If Joe starts school in September, then he lives in New York state.

(b) If Joe does not live in New York State, then he does not start school in September.

(c) If Joe starts school in September, then he does not live in New York State.

(d) If Joe lives in New York State, then he starts school in September

4) Given this true statement:

“Mark is seventeen years old or Mindy is fifteen years old.”

What could be true about the ages of Mark and Mindy?

(a) Mark is 17 and Mindy is 15.

(b) Mark is 16 and Mindy is 16.

(c) Mark is 18 or Mindy is 17.

(d) Mark is 18 or Mindy s 16.

5) What is the inverse of the statement: “If Bob gets hurt, then the team loses the

game.” (a) If the team loses the game, then Bob

gets hurt. (b) Bob gets hurt if the team loses the

game. (c) If the team does not lose the game,

then Bob does not get hurt. (d) If Bob does not get hurt, then the

team does not lose the game.