Question

In: Computer Science

Two compound propositions p and q in propositional logic are logically equivalent if . . ..

Complete the following statements.

Two compound propositions p and q in propositional logic are logically equivalent if . . ..

An argument form in propositional logic is valid if . . ..

A theorem is a statement that . . ..

A statement that is assumed to be true is called a(n) . . ..

A proof is a valid argument that . . ..

Solutions

Expert Solution

Two compound propositions p and q in propositional logic are logically equivalent if they always have the same truth value.

An argument form in propositional logic is valid if ll the premises are true (are satisfied), the conclusion is also true.

A theorem is a statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis previously established statements such as other theorems.

A statement that is assumed to be true is called a(n), to serve as a premise or starting point for further reasoning and arguments.

A proof is a valid argument that uses some form of logic (usually predicate logic) and uses logical rules of deduction and axioms or theorems in it's specific field to drive some new sentences that will eventually lead to the proposition we want to prove .


Related Solutions

Use the laws of propositional logic to prove that the followingcompound propositions are logically equivalent....
Use the laws of propositional logic to prove that the following compound propositions are logically equivalent.A. ? ↔ (? ∧ ?) and ? → ?B. ¬(? ∨ (? ∧ (? → ?))) and ¬? ∧ (? → ?)
Use the laws of propositional logic to prove that the following compound propositions are tautologies. ((?...
Use the laws of propositional logic to prove that the following compound propositions are tautologies. ((? → ?) ∧ (? → ?)) → (? → ?)
Use the laws of propositional logic to prove that the following compound propositions are tautologies. ((?...
Use the laws of propositional logic to prove that the following compound propositions are tautologies. ((? → ?) ∧ (? → ?)) → (? → ?)
Consider a formula of propositional logic consisting of a conjunction of clauses of the form (±p⊕±q),...
Consider a formula of propositional logic consisting of a conjunction of clauses of the form (±p⊕±q), where p and q are propositional variables (not necessarily distinct) and ±p stands for either p or ¬p. Consider the graph in which the vertices include p and ¬p for all propositional variables p appearing in the formula, and in which there is an edge (1) connecting p and ¬p for each variable p, and (2) connecting two literals if their exclusive-or is a...
Prove the validity using laws of propositional logic and rules of inference: ∀x(P(x) → (Q(x) ∧...
Prove the validity using laws of propositional logic and rules of inference: ∀x(P(x) → (Q(x) ∧ S(x))) ∃x(P(x) ∧ R(x)) − − − − − − − − − − − − − ∴ ∃x(R(x) ∧ S(x))
Represent the following in propositional logic. Label the component propositions. Note you may have to reword...
Represent the following in propositional logic. Label the component propositions. Note you may have to reword some propositions. Bread contains carbs and so does rice. Either John or Chris was the first student in class this morning. I have a bad shoulder and whenever it is raining, my shoulder aches. If the weather is nice, then if Dr Marlowe is lecturing, we will sleep in and then go for a hike. Henry will stay in his job only if he...
Use the laws of propositional logic to prove that the following compound proposition is a tautologies...
Use the laws of propositional logic to prove that the following compound proposition is a tautologies (¬? ∧ (? ∨ ?)) → ?
Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.)...
Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.) Why does this equivalency allow us to use the proof by contradiction technique?
FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT p=q p=(s→(p ∧¬r)) ∧...
FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT p=q p=(s→(p ∧¬r)) ∧ ((p→(r ∨ q)) ∧ s), Q=p ∨ t
Conceptually the two most common logics are propositional logic and Predicate Logic. An undergraduate student who...
Conceptually the two most common logics are propositional logic and Predicate Logic. An undergraduate student who took a course of discrete mathematics is inquiring as to how propositional and predicate logics can be used in software testing. How are ask to guide this student in this quest. One pointer may consist in presenting the characteristics and limitations of both logic as well as their use as a mean for software testing. Which Logic is most adequate for formal verification of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT