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MODULE 2: ELEMENTARY LOGIC:CONNECTIVES, QUANTIFIERS, NEGATIONS AND VARIABLES. Historical Note: Logic is the science of correct thinking. One of the first mathematicians to make serious study of symbolic logic was Gottfried Wilhelm Leibniz (1646- 1716).
NEGATIONS If p is a statement, the negation of p is another statement that is exactly the opposite of p. The negation of a statement p is denoted ~p ("not p"). A statement p and its negation ~p will always have opposite truth values; it is impossible to conceive of a situation in which a statement and its negation will have the same truth value ...
When we negate a statement with a universal quantifier, we get a statement with an existential quantifier, and vice-versa. Negating a Quantified Statement The negation of “all A are B” is “at least one A is not B”.
When we negate a statement with more than one quantifier, we consider each quantifier in turn and apply the appropriate part of Theorem 2.16. As an example, we will negate Statement (3) from the preceding list.
Quantifiers and Negation. For all of you, there exists information about quantifiers below. We often quantify a variable for a statement, or predicate, by claiming a statement holds for all values of the quantity or we say there exists a quantity for which the statement holds (at least one).
In other words, a statement is a sentence whose truth value is definite, in more other words, it is always possible to decide – one way or the other – whether a statement is true or false. 2 The first example of a sentence given above (“Johnny was a football player”) is not a statement – the problem is that it is ambiguous unless we know who Joh...
We have already studied connectives; in this section we introduce name letters, predicates, variables, and quantifiers. In our logical symbolism, name letters are written as the small letters: a, b, c, d, e, f, g, h (and with subscripts, such as ‘c3’). Any small letter between 'a' and 'h' can be used as a name letter.
