Logically equivalent statement
[DOC File]Truth Tables, Tautologies, & Logically Equivalent Statements:
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Logically Equivalent Statements: When two statements always have the same truth values, we say that the statements are logically equivalent. To show that equivalence exists between two statements, we use the biconditional if and only if. If the statements always have the same truth values, then the biconditional statement will be true in every case, resulting in a tautology. Let p represent ...
[DOC File]Computer Science 1MD3
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We say that the propositions p, and q are logically equivalent if is a tautology, or in other words, it will always evaluate to true. The notation denotes that p and q are logically equivalent. One way to determine whether two propositions are equivalent is to use a truth table. In particular, the propositions p and q are equivalent if and only if the columns giving their truth-value agree ...
[DOC File]St. Francis Preparatory School
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Which ones is logically equivalent to the original statement? contrapositive For the questions below use the following statements: Let p represent: Friends was a TV show. Let q represent: Gossip Girl is on Tuesday nights. Let r represent: A dog is not an animal. Let s represent: All triangles have four sides.
[DOC File]Equivalent Statements
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Figure 1 represents the original conditional statement and the contrapositive of the original. Key Point : The original conditional statement and the contrapositive of the original are logically equivalent statements and may be used interchangeably. p → q is logically equivalent to ~q → ~p. p → q may be replaced by ~q → ~p. ~q → ~p may be replaced by p → q.
[DOC File]SI202: Week 1
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A conditional statement is logically equivalent to its contrapositive. Examples: Write each of the following in its equivalent contrapositive form. If today is Wednesday then tomorrow is Thursday. If the temperature goes up then it will be hotter. If today is Friday then I have a quiz today . Suppose we have the conditional p q . The contrapositive is ~ q ~ p which, in English, is . Think ...
[DOC File]Translate the following sentences into the standard (= “if ...
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This statement is logically equivalent to our original conditional statement, put in standard form: “ If. Moby Dick is a whale, then Moby Dick is a mammal.” In both cases, “Moby Dick is a mammal.” is the consequent of the conditional statement. Here, think of the “only if” in a conditional statement as saying that the consequent must be true for the antecedent to be true as well ...
[DOC File]MODULE 1 - Department of Mathematics
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Statement Equivalent form . p and q q and p . p or q q or p . p or q If not p then q Negations (DeMorgan's Laws) Statement Negation . p and q not p or not q . p or q not p and not q . EXAMPLE 2.1.21. Select the statement that is logically equivalent to "I'm careful or I make mistakes." A. I'm careful and I make mistakes. B. I make mistakes and ...
[DOC File]Math 180 Exercises
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Definition 1.1 : Statement A is logically equivalent to statement B, written, A ( B when A ( B. Definition 1.2 : Statement A is the logical opposite of statement B iff A ( (B (and (A ( B). 1. Construct a compleat truth table for the following statements, identify which statements are logically equivalent, and which statements are logical opposites:
[DOC File]Converse: - University of Northern Iowa
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Conversion can be applied to any particular affirmative or universal negative categorical proposition to yield a logically equivalent proposition. Converse: PA statement converse (PA) UN statement converse (UN) Sentence logic: S ( P = S ( P S ( (P = P ( (S. Predicate logic: ((x)(Sx (Px) = ((x)(Px ( Sx) (x)(Sx ( (Px) = (x)(Px ( (Sx) Categorical logic: Some S is P = Some P is S No S are P = No P ...
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