What is logic?
No matter what you study, chances are that you’ll be required to use and understanding logic as you convey your ideas and process the ideas of others in your field. And one of the components of the SAT Essay task is to analyze how an author uses logic, evidence, and rhetoric to persuade a reader. So today’s article is centered around logic. What is logic? What types of logical statements can we make? Read on to learn about 6 types of logical statements and how to construct and interpret them!
6 Types of Logical Statements to Know
1) Simple logical statement
As its name suggests, simple statements are, well, simple. They posit the truth of one idea, and they do so using one simple sentence. Let’s take a look at a couple of examples:
Antarctica is the southernmost continent on the globe.
Penguins cannot fly.
The key is in the room.
The dog’s asleep.
Notice that the sentences above vary in their length, but at their heart, they each express one simple idea. They’re each making one claim, and that claim is easy to understand. When analyzing the logic of simple logical statements, we must understand what they’re claiming and assess whether that claim is true or false.
Another type of logical statement is the conjunction. Conjunctions are compound sentences, and they consist of two or more simple sentences joined by the word “and” (or any of the other conjunctions, such as “but,” “yet,” “so,” and so on…) Conjunctions express two ideas, and are slightly more complex than simple logical statements. Each of the separate independent clauses within the conjunction is a called a “conjunct.” Let’s take a look at a couple of examples of conjunctive logical statements.
The dog is asleep, but the cat is awake.
I tried hard, yet I failed.
The forecast shows it’s going to rain, so I’m going to bring an umbrella.
Notice that the two ideas complicate one another. The logic of the conjunction depends not only on the ideas contained in each of the conjuncts but also in the conjunction that connects the two ideas. For example, the word “and” will indicate a different logical relationship than the word “but,” which will indicate a different logical relationship than the word “so.” Pay close attention to the meaning of each of the conjuncts, and pay attention to the logical relationship conveyed by the conjunction itself. The three broad types of conjunctions are “continuers,” which add information, “contradictors,” which show contrast or counterpoint, and “cause and effect,” which shows a cause-and-effect relationship.
Disjunctions are compound sentences consisting of two simple sentences connected with the words “either/or,” “or,” or “unless.” The logic that disjunctions convey is different than the logic that conjunctions convey, so pay attention to the author’s use of conjunctions to follow his or her logic. Disjunctions indicate two possibilities that are exclusive from one other; that is, they suggest that one of the propositions is true, but not both. Let’s take a look at some examples of disjunctions:
Either it will rain, or it won’t.
Either you’re with us, or you’re against us.
I’m going to finish my essay tonight, unless I decide to watch Netflix instead.
Each of the separate independent clauses in a disjunction is called a “disjunct.” Notice that one of the disjuncts can be true, but not both, according to the logic conveyed in the disjunction’s conjunction.
Conditional statements require conditions to be true. Conditional statements are a great way to explain logic, because they make connections between ideas. They take the form of an “if/then” statement. By their nature, conditional statements are hypothetical. They posit that IF one thing is true, THEN another thing must follow. Closely pay attention to the claims conditional statements are making when you evaluate whether or not they’re logically sound. Here are a couple of examples of conditional statements:
If it rains, then we will postpone our trip.
If you’re hungry, then you should have a snack.
If it’s possible to get a perfect score on the SAT, then you should do so.
Notice how one part of the statement depends on the other to be true in order for it to be true. Pay special attention to which part of the conditional statement is the condition and which is the effect of that condition. The two parts of the conditional statement are called the “antecedent” and the “consequent.” The antecedent is the “if” clause, and the consequent is the “then” clause.
Slightly more emphatic than the conditional statement is the biconditional statement. Like its name suggests, the biconditional statement contains two conditionals, but each of those conditional implies and suggests the other. Biconditionals usually take the form of “if and only if” statements. Other words besides “if and only if” that indicate the presence of a biconditional statement are “implies and is implied by,” “entails,” and “just in case that.” Let’s take a look at a couple examples of biconditional statements:
The test will include questions on Hamlet, if and only if we have time to discuss it in class.
The fact that you passed the test implies and is implied by the fact that you got a 70 or above on it.
A shape is a triangle if and only if it has three sides.
A hexagon is regular if and only if its angle measures and side lengths are the same.
The last type of sentence we’ll examine today is the negation. A negation is the opposite of an affirmation or positive statement. Rather than asserting the truth of a proposition, a negation explicitly DENIES that a proposition is true, thus negating it. There are a variety of ways in which you can deny a proposition using a negation, such as using the phrases “not,” “never,” “it is false that,” and so on. Let’s take a look at a couple of negations:
The world isn’t flat.
Money can’t buy love.
It is false that tomatoes are vegetables.
Once you understand these 6 types of logical statements, you’ll be well on your way to expressing logical statements of your own. And when the time comes to evaluate whether or not a proposition is logically sound, you’ll be ready.
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That’s it! Now that you understand the 6 types of logical statements, you’ll be better equipped to make logical statements of your own. Good luck! For more great articles, as well as a plethora of SAT and ACT prep tips, check out the rest of our blog. Looking for 1-on-1 ACT or SAT prep tutoring to help you with the college application process? Want to join an SAT or ACT group class? Contact us today! We’re perfect-scoring tutors with years of experience helping students achieve the SAT and ACT scores they need to make their dreams a reality!