The statements that are related in this way are considered logically equivalent.įor example, consider the statement, “If it is raining, then the grass is wet” to be TRUE. If we know that a statement is true (or false), then we can assume that another is also true (or false). How is this helpful? The key is in the relationship between the statements. You may be wondering why we would want to go through the trouble of rearranging and considering the “opposite” of the hypothesis and conclusion statements. Our contrapositive statement would be: “If the grass is NOT wet, then it is NOT raining.”.Our inverse statement would be: “If it is NOT raining, then the grass is NOT wet.”.Our converse statement would be: “If the grass is wet, then it is raining.”.Now we can use the definitions that we introduced earlier to create the three other statements. The notation associated with conditional statements typically uses the variable \(p\) for the hypothesis statement, and \(q\) for the conclusion. The second statement is linked with “then”, and is known as the conclusion. The first statement is presented with “if,” and is referred to as the hypothesis. Two independent statements can be related to each other in a logic structure called a conditional statement. This declarative statement could also be referred to as a proposition. For example, a declarative statement pronounces a fact, like “the Sun is hot.” We know this is a statement because the Sun cannot be both hot and not hot at the same time. Let’s first take a look at a basic statement, which can be either true or false, but never both. These, along with some reasoning skills, allow us to make sense of problems presented in math. Specifically, we will learn how to interpret a math statement to create what are known as converse, inverse, and contrapositive statements. Hi, and welcome to this video on mathematical statements! Today, we’ll be exploring the logic that appears in the language of math.
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