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If $p\implies q$ ("$p$ implies $q$"), then $p$ is a sufficient condition for $q$. If $\lnot p\implies \lnot q$ ("not $p$ implies not $q$"), then $p$ is a necessary condition for $q$. I don't under...
- Conditional Statement
- Biconditional Statement
- Translating Statements and Symbolic Logic
- Converse, Inverse, and Contrapositive
- Truth Values and Truth Tables
- Logical Implication – Lesson & Examples
Here are a few examples of conditional statements: “If it is sunny, then we will go to the beach.” “If the sky is clear, then we will be able to see the stars.” “Studying for the test is a sufficient condition for passing the class.” Here’s a typical list of ways we can express a logical implication: 1. If p, then q 2. If p, q 3. p is sufficient fo...
Now, another necessary type of implication is called a biconditional statement. A biconditional statement, sometimes referred to as a bi-implication, may take one the following forms: 1. P if and only if q 2. P is necessary and sufficient for q 3. If p then q, and conversely 4. P iff q, where “iff” stands for “if and only if” And the biconditional ...
Additionally, we will discover six different types of sentences in propositional logic, and we will learn how to translate from English to symbols and vice versa with ease.
Furthermore, we will learn how to take conditional statements and find new compound statements in the converse, inverse, and contrapositive form. For example, let’s suppose we have the proposition: “If the card is a club, then it is black,” has a very different truth value than “if the card is black, then it is a club.” The first conditional statem...
And being able to verify the truth value of conditional statements and its inverse, converse, and the contrapositive is going to be an essential part of our analysis. Consider the implication: if n is an odd integer, then 5n+1 is even. Write the converse, inverse, contrapositive, and biconditional statements. 1. Converse: if 5n+1 is even, then n is...
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A conditional statement is a statement that is written in the form "If p, then p."It’s denoted by p → q. Learn the definition, truth table, examples, and more.
- Conditional statements, also known as \"if-then\" statements, express a cause-and-effect or logical relationship between two propositions.
- A conditional statement is considered false when the antecedent is true and the consequent is false.
- The contrapositive reverses the order of the statements and also negates both the statements. It is equivalent in truth value to the original state...
The statement P is called the hypothesis of the conditional statement, and the statement Q is called the conclusion of the conditional statement. Since conditional statements are probably the most important type of statement in mathematics, we give a more formal definition.
The statement \(p\) in an implication \(p \Rightarrow q\) is called its hypothesis, premise, or antecedent, and \(q\) the conclusion or consequence. Implications come in many disguised forms. There are several alternatives for saying \(p \Rightarrow q\).
For the example P above, ∼ P is the statement,‘’five is not less than eight’, or ’five is greater than or equal to eight’. For an arbitrary mathematical statement P, we can indicate the possible truth
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The biconditional – “p iff q” or “p if and only if q”. If and only if statements, which math people like to shorthand with “iff”, are very powerful as they are essentially saying that p and q are interchangeable statements. When one is true, you automatically know the other is true as well.
