Presentation on theme: "3 Logic The Study of What’s True or False or Somewhere in Between."— Presentation transcript:
13LogicThe Study of What’s True or False or Somewhere in Between
23.2Truth TablesLearn the truth tables for the five fundamental connectivesCompute truth tables for compound statements(continued on next slide)
33.2 Truth Tables Determine when statements are logically equivalent State and apply DeMorgan’s laws.
4Truth TablesWe want to know if a pair of similar statements such as and mean the same thing.We use truth tables to determine when compound statements are true and when they are false, and whether a pair of statements have the same meaning.
15Truth TablesBecause of their similar structures, there are parallels that occur in logic and set theory.Often if a result is true for set theory, then a similar result also holds for logic (and vice versa).
16Compound StatementsWe use truth tables to find the logical values of complex statements.Example: Compute a truth table for(solution on next 3 slides)
17Compound Statements(solution continued on next slide)
18Compound Statements(solution continued on next slide)
19Compound StatementsIf p is false and q is true, line 3 tells us that is false.
20Compound StatementsDefinition: If the final column of a truth table contains all T’s, then the statement is always true. Such a statement is called a tautology.Example: “This contestant will win or will not win.”
21Compound StatementsHow many lines should your truth table have?
22Logically Equivalent Statements Logically equivalent statements express the same meaning.(example on next slide)
23Logically Equivalent Statements Example:(solution on next slide)
24Logically Equivalent Statements Solution:The two statements are logically equivalent.