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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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Outline. Propositions. proposition is a declarative sentence that is either true or false. Examples of propositions: The Moon is made of green cheese. Trenton is the capital of New Jersey. Toronto is the capital of Canada. + 0 = 1. 0 + 0 = 2 Examples that are not propositions. Sit down! What time is it? x + 1 = 2. x + y = z. Propositional Logic.
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Direct proofs are especially useful when proving implications. The general format to prove P → Q P → Q is this: Assume P. P. Explain, explain, …, explain. Therefore Q. Q. Often we want to prove universal statements, perhaps of the form ∀x(P (x)→ Q(x)). ∀ x (P (x) → Q (x)).
Mixed exam-style questions on partial fractions - Answers. 13a. Mixed exam-style questions on rational expressions. 13b. Mixed exam-style questions on rational expressions - Answers. Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Algebra and Functions.
The statement p in an implication p ⇒ 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 ⇒ q. The most common ones are. p implies q, p only if q, q if p, q, provided that p. All of them mean p ⇒ q.
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Jan 19, 2021 · Conditional statements are also called implications. The statement is an implication p -> q is called its hypothesis, and q the conclusion. Example: Let p be the statement “Maria learn Java Programming ” and q is the statement “Maria will find a good job”.
