Classwork/Homework Classwork – Page 90 (11 – 49 odd) Homework – Page 90 (12 – 50 even)

2.3 Truth Tables Learn the truth tables for the five fundamental connectives. Compute truth tables for compound statements. Determine when statements are logically equivalent. State and apply DeMorgan’s laws.

Negating a statement reverses its truth value. If p is a true statement, then its negation is false. If p is a false statement, then its negation is true. p ~ p T F Possible truth values for statement p. Logical truth values for ~ p.

A conjunction is true only when both of its component parts are true. The and connective also works in logic as it does in everyday life. In order for the conjunction to be true, both parts (p and q) need to be true. p q p ^ q T F

A disjuction is false only when both of its component parts are false. Mathematicians use the word or slightly differently then we use or in everyday life. In everyday conversation, we use the exclusive or (one or the other, but not both). In logic, we use the inclusive or (one or the other or both). p q p q T F

We use truth tables to find the logical values of complex statements. When calculating truth tables of compound statements, you also have to pay attention to the order in which you perform logical operations. Tautology – a statement that is always true. If a statement has k variables, then its truth table will have 2k lines.

Logically equivalent statements express the same meaning. Two statements are logically equivalent if they have the same variables and, when their truth tables are computed, the final columns in the tables are identical. DeMorgan’s laws for logic: if p and q are statements, then ~ (p q) is logically equivalent to (~ p) (~ q) ~ (p q) is logically equivalent to (~ p) (~ q)

There is an alternative way to construct truth tables. Truth table for ( ~ p q) (p q) Method 1 1 2 3 4 p q ~ p ~ p ^ q p ^ q (~ p ^ q) (p ^ q) T F

Method 2 Truth table for ( ~ p q) (p q) 1 2 4 3 p q ( ~ q) (p T F

Classwork/Homework Classwork – Page 102 (29 - 33 odd, 37 - 41 odd) Homework – Page 102 (30 - 34 even, 38 – 42 even)

Classwork/Homework Classwork – Page 102 (37 – 45 odd, 61 – 67 odd) Homework – Page 102 (38 – 48 even, 62 – 68 even)