23CS2501 -Logical and Critical thinking | URK23CS1224 Ex no: | PROPOSITIONAL LOGIC AND TRUTH TABLES Date 18:09:2023 AIM: To understand the proposition logic and translate the English sentences into formal language using conjunction (the dot), negation (the tilde), or disjunction (the wedge) and write the truth table. DESCRIPTION Propositional logic (also called “sentential logic") is the area of formal logic that deals with the logical relationships between propositions. Some examples of proposi ons are Snow is white Snow is cold ‘Tom is an astronaut ‘The floor has been mopped ‘The dishes have been washed Complex proposition We can also connect propositions together using certain English words, such as “and” like this: ‘The floor has been mopped and the dishes have been washed. This proposition is called a complex proposition because it contains the connective “and” which connects two separate propositions. Atomic propositions are those that do not contain any truth-functional connectives. A truth-finetional connective is a way of connecting propositions such that the truth value of the resulting complex proposition can be determined by the truth value of the propositions that compose it, ‘The basic truthefunctional connectives are conjunetion, disjunction, negation23CS2501 -Logical and Critical thinking | URK23CS1224 Conjunction In the formal language that we are developing we will represent conjunctions using a symbol called the “dot,” which looks like thi Using this symbol, here is how we will represent a conjunction in symbolic notation: pea Negation is the truthefunctional operator that switches the truth value of a proposition from false to true or from true to false. For example, if the statement “dogs are mammals” is true (which it is), then we can make that statement false by adding a negation. The symbol we will use to represent negation is called the “tilde” (~). A disjunction is a truth-functional statement that is true in every instance except where both of the disjuncts are false. Ih our symbolic language, The symbol we will use to represent a disjunction is called a “wedge” ().(You can simply use a lowercase “V" to write the wedge.) EXERCISE: I. Translate the following English sentences into our formal language using conjunction (the dot), negation (the tilde), or disjunction (the wed ge) and write the truth table, 1. Either Bob will mop or Tom will mop. (B = Bob will mop; BvT ~ disjunction = Tom will mop) BT [Br F[FI[F Ff{[t[t TIFT Ti[T{T 2. [tis not sunny today. (S = it is sunny today) ~S~—negation Ss |-S F/T23CS2501 -Logical and Critical thinking | URK23CS1224 3. It is not the case that Bob is a burglar. (B = Bob is a burglar) ~B - mgation 4. Harry is arriving either tonight or tomorrow night. (A = Harry is arriving tonight; B = Harry is arriving tomorrow night) ANB - disjunction 5. Gareth does not like his name. (G = Gareth likes his name) ~G -regation23CS2501 -Logical and Critical thinking | URK23CS1224 6. Bither it will not rain on Monday or it will not rain on Tuesday. (M = I will rain on, Monday; T = It will rain on Tuesday) MvT - disjunction M | tT [vr | -Mvr 7. Tom does not like cheesecake. (T = Tom likes chee ~T - negation v |r 8, Bob would like to have both a large cat and a small dog as a pet, (C =Bob would like to have a large cat as a pet; D = Bob would like to have a small dog as a pet) C.D = conjunction23CS2501 -Logical and Critical thinking | URK23CS1224 9, Bob Saget is not actually very funny. (B = Bob Saget is very funny) ~B - megation B ~B F T . 10. Albert Einstein did not believe in God. (A = Albert Einstein believed in God) ~A- negation RESULT: ‘The given sentences are translated into formal language using conjunction, disjunction and negation,