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Mar 4, 2024 · A converse statement is a proposition formed by interchanging the hypothesis and conclusion of a conditional statement. In simpler terms, it’s like flipping the order of “if” and “then” in a statement. For example, in the conditional statement “If it is raining, then the ground is wet”, the converse statement would be “If the ...
Example: Consider the following conditional statement. If a number is a multiple of 8, then the number is a multiple of 4. Write the contrapositive and converse of the statement.
Nov 28, 2020 · The contrapositive is logically equivalent to the original statement. The converse and inverse may or may not be true. When the original statement and converse are both true then the statement is a biconditional statement. In other words, if p → q is true and q → p is true, then p ↔ q (said “ p if and only if q ”).
Example 2.3.1 2.3. 1: Related Conditionals are not All Equivalent. Suppose m m is a fixed but unspecified whole number that is greater than 2. 2. conditional. If m m is a prime number, then it is an odd number. contrapositive. If m m is not an odd number, then it is not a prime number. converse.
- Negation
- Converse, Contrapositive, and Inverse
- Logical Equivalence
Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. Every statement in logicis either true or false. The negation of a statement simply involves the insertion of the word “not” at the proper part of the statement. The addition of the word “not” is done so that it changes t...
Now we can define the converse, contrapositive, and inverse of a conditional statement. We start with the conditional statement “If P then Q.” 1. The converse of the conditional statement is “If Q then P.” 2. The contrapositive of the conditional statement is “If not Q then not P.” 3. The inverse of the conditional statement is “If not P then notQ....
We may wonder why it is important to form these other conditional statements from our initial one. A careful look at the above example reveals something. Suppose that the original statement “If it rained last night, then the sidewalk is wet” is true. Which of the other statements have to be true as well? 1. The converse “If the sidewalk is wet, the...
Jan 11, 2023 · Fricasé de Pollo is a type of Cuban food. Statements 2 and 4 are logical statements; statement 1 is an opinion, and statement 3 is a fragment with no logical meaning. Four testable types of logical statements are converse, inverse, contrapositive, and counterexample statements. They can produce logical equivalence for the original statement ...
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A converse statement is the opposite of a conditional statement. It is to be noted that not always the converse of a conditional statement is true. For example, in geometry , "If a closed shape has four sides then it is a square" is a conditional statement, The truthfulness of a converse statement depends on the truth of hypotheses of the conditional statement.
