
1 Deductive Reasoning and Logical Connectives
... Example 7 Write negations for each of the following statements: • John is 6 feet tall and he weighs at least 200 pounds. • The bus was late or Tom’s watch was slow. • x ≮ 2 where x is a real number. • Jim is tall and Jim is thin. Note: For the last example, “Jim is tall and Jim is thin” can be writt ...
... Example 7 Write negations for each of the following statements: • John is 6 feet tall and he weighs at least 200 pounds. • The bus was late or Tom’s watch was slow. • x ≮ 2 where x is a real number. • Jim is tall and Jim is thin. Note: For the last example, “Jim is tall and Jim is thin” can be writt ...
A mathematical sentence is a sentence that states a fact or contains
... a) Using s and c and proper logic connectives, express each of the following sentences in symbolic form. If Simon takes chorus, then he cannot take Spanish. If Simon takes Spanish then he cannot take chorus. b) Prove that the two statements are logically equivalent, or give a reason why they are not ...
... a) Using s and c and proper logic connectives, express each of the following sentences in symbolic form. If Simon takes chorus, then he cannot take Spanish. If Simon takes Spanish then he cannot take chorus. b) Prove that the two statements are logically equivalent, or give a reason why they are not ...
Chapter One {Word doc}
... It is important to realize that one of the difficulties in translating back and forth from English (or any other natural language) to symbolic logic comes from the fact that some expressions are used in more than one way, logically speaking. In addition it is difficult to disambiguate because closel ...
... It is important to realize that one of the difficulties in translating back and forth from English (or any other natural language) to symbolic logic comes from the fact that some expressions are used in more than one way, logically speaking. In addition it is difficult to disambiguate because closel ...
Truth, Conservativeness and Provability
... → ϕ’), which is obviously stronger then S itself. On Tennant’s view this however should not be treated as a shortcoming of the proposed solution. On the contrary—the aim here is to present a realistic description of how the deflationist could arrive at stronger theories without burdening himself wit ...
... → ϕ’), which is obviously stronger then S itself. On Tennant’s view this however should not be treated as a shortcoming of the proposed solution. On the contrary—the aim here is to present a realistic description of how the deflationist could arrive at stronger theories without burdening himself wit ...
Exercise
... P(x) it is not enough to show that P(a) is true for one or some a’s. 2. To show that a statement of the form x P(x) is FALSE, it is enough to show that P(a) is false for one a ...
... P(x) it is not enough to show that P(a) is true for one or some a’s. 2. To show that a statement of the form x P(x) is FALSE, it is enough to show that P(a) is false for one a ...
Chapter 2 Propositional Logic
... • Example: ‘Bob pays taxes only if his income ≥ $1000’ ≜ ‘if Bob’s income < $1000 then he does not pay taxes’ ≡ ‘if Bob pays tax then his income ≥ $1000’ ...
... • Example: ‘Bob pays taxes only if his income ≥ $1000’ ≜ ‘if Bob’s income < $1000 then he does not pay taxes’ ≡ ‘if Bob pays tax then his income ≥ $1000’ ...
Lesson 2
... • Hence if we prove that the conclusion logically follows from the assumptions, then by virtue of it we do not prove that the conclusion is true • It is true, provided the premises are true • The argument the premises of which are true is called sound. • Truthfulness or Falseness of premises can be ...
... • Hence if we prove that the conclusion logically follows from the assumptions, then by virtue of it we do not prove that the conclusion is true • It is true, provided the premises are true • The argument the premises of which are true is called sound. • Truthfulness or Falseness of premises can be ...
Logic Review
... and you didn’t come to class on time.” When is this statement false? When either you did your homework or you came to class on time. ...
... and you didn’t come to class on time.” When is this statement false? When either you did your homework or you came to class on time. ...