Question

6.1 Aplia Assignment 16. True or False? Use your knowledge of propositional logic symbols and translation methods to determine which of the fol apply. O "Either..., or..." statements are usually best translated as disjunctions with the wedge (V) oper O A dot (•) is the main operator in this statement: Q v mW). ( P L ) The triple bar () operator expresses the logical relation of material implication. In propositional logic, the fundamental elements are terms. O A horseshoe () is the main operator in this statement: [(S G F). ). O] ( E O The following expression is a well-formed formula (WFF): -( wl). [(x = -X).O]. O You should translate the statement "Today is Wednesday only if tomorrow if Thursday" into pr W stands for "Today is Wednesday," and T stands for "Tomorrow is Thursday." O The tilde (-) operator is always placed between the two statements it connects. O The statements ( A B) and A B are equivalent according to De Morgan's Rule. The statement A B is equivalent to the statement B A O The antecedent of a conditional represents a necessary condition O You should translate the statement "Today is Wednesday if tomorrow is Thursday" into propos stands for "Today is Wednesday," and T stands for "Tomorrow is Thursday." O You should translate an ordinary language statement with the form "p only if " into propositi You should translate an ordinary language statement with the form "p only if q' into propositi You should translate the statement "Not both today is Wednesday and tomorrow is Friday" int where W stands for "Today is Wednesday," and F stands for "Tomorrow is Friday."

Answer 1

1. True - Operator 'v' (Wedge)

Logical function: disjunction; translates: "or", "unless", "either...or"; states that either both statements are not true, or at least one statement is false, and the other is true; used medially to both statements; ex: "Either is it Saturday, or it is Friday" becomes "S v F", where "Saturday"=S, and "Friday"=F.

2. True - Dot Logical function: conjunction; translates: "and", "also", "moreover", "both", "however", etc.; affirms both statements; ex: "It is spring and pleasant" becomes "S•P", where "It is spring"=S, and "pleasant"=P; used medially to both statements.

3. False :

Propositional Logictriple bar ≡

equivalence/biconditional: if and only if, equivalent to, sufficient and necessary condition for.

4. False :

The fundamental components are statement themselves, and are represented by capital letters; statements are connected by operators; can be a simple statement or a compound statement.