Conjunctive sentence linkages are words or phrases that are used to connect two independent clauses in a sentence. They help to show the relationship between the two clauses, such as addition, contrast, cause and effect, or time sequence. Common conjunctive sentence linkages include words like "and," "but," "because," "however," "therefore," and "meanwhile." Using conjunctive sentence linkages helps to create smooth and coherent transitions between ideas in a sentence or paragraph. **

A conjunctive subordinate clause is a type of dependent clause that begins with a subordinating conjunction, such as "although," "because," "while," or "since." These clauses cannot stand alone as complete sentences and must be attached to an independent clause to form a complete sentence. They provide additional information or context to the main clause and help to show the relationship between the two clauses. For example, in the sentence "Although it was raining, we still went for a walk," the clause "Although it was raining" is a conjunctive subordinate clause. **

No, conjunctive clauses are not always adverbial clauses. While adverbial clauses are a type of conjunctive clause that function as adverbs to modify verbs, adjectives, or other adverbs, there are also other types of conjunctive clauses. For example, there are conjunctive clauses that function as noun clauses, such as in "I know that you are busy." In this sentence, "that you are busy" is a conjunctive clause functioning as a noun clause, not an adverbial clause. Therefore, conjunctive clauses can serve various grammatical functions beyond just adverbial clauses. **

To form the conjunctive normal form (CNF) of a logical expression, first convert the expression into its disjunctive normal form (DNF). This involves applying the distributive law to expand the expression into a sum of products. Then, distribute any negations to push them down to the individual variables. Finally, combine the products of variables with OR operations to form the CNF, which is a conjunction of clauses, each of which is a disjunction of literals. **

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To convert a formula into conjunctive normal form (CNF), you first need to eliminate implications and bi-conditional connectives by using logical equivalences. Then, you can distribute negations inwards using De Morgan's laws. After that, you can use the distributive law to move disjunctions inside conjunctions. Finally, you can distribute conjunctions over disjunctions to ensure that the formula is in CNF, which consists of a conjunction of clauses, where each clause is a disjunction of literals. **

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