Practice Your Skill 2.2 Write the following in roster form. Set of all fingers Set of all oceans in the world Describe the following sets by its property {1,3,5,7,9} {liquid, gases, solid, plasma} If f(x)=3x+2, find f(2) its inverse. Elementary Logic Logical Connectives A logical connective is the mathematical equivalent of a conjunction. That is, it is a word (or symbol) that joins two sentences to produce a new one. If P and Q are propositions, then P∧Q (conjunction) is the statement that is true if and only if both P and Q are true. Otherwise, P and Q are false. A proposition is a statement that is either true or false but not both. Another connective is the word “or,” and its symbol is "∨". The statement P∨Q (disjunction) …show more content…
2=3≠5 Quantifiers Quantifiers are words that indicate the amount or numbers being referred to. Words such as “all,” “some,”, “every,” “a few” and “nothing” are examples of quantifiers. In English language, there are several quantifiers. However, this leads to some sort of ambiguity. As such, Mathematicians therefore limit to only two quantifiers: the universal quantifier “for all” (or for every) and existential quantifier “there exists” (or for some). In order for us to write complicated mathematical sentences in a highly symbolic form, the symbols ∀ and ∃ are used to denote “for all” and “there exists,” respectively. Example 2.14: Use quantifiers to express the following statements: Every college student needs to take up Mathematics in the Modern World. There is a student in this class who graduated valedictorian. Solution: Let P(x) denote the statement “x needs to take up Mathematics in the Modern World.” The given statement can now be expressed as ∀x P(x) where the domain of discourse consists of the college students. Let Q(x) denote the statement “x who graduated valedictorian.” The given statement can now be expressed as ∃x Q(x) where the domain of discourse consists of students in this
Symbolism can be defined as “the representation of a reality on one level of reference by a corresponding reality on another” (“Symbolism” 564). The word symbol comes from the Greek word "symballein," which translates literally into “to throw together” and suggests the combining of two unrelated worlds. Much...
A symbol in literature is an object that stands for a word, cause, belief, or another object. A metaphor is a figure of speech where a word of phrase is applied to something but it should not be taken literally. In the book To Kill a Mockingbird, the mockingbird symbolizes innocence. The mockingbird is innocent, singing for people to hear its music. In the book Atticus says to Scout, “Remember it is a sin to kill a mockingbird.” When Scout asked Miss Maudie about it, Miss Maudie tells her, “Mockingbirds don’t do one thing but make music for us to enjoy… but they sing their hearts out for us. That’s why it’s a sin to kill a mockingbird.” Killing something so innocent would be a sin because it had never done anything to hurt you.
Fromm, Erich. “The Nature of Symbolic Language.” Class Handout: English 101. Cerro Coso Community College, 2010. 121-26. Print.
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas or visual images and are used to convey other ideas and beliefs. A symbol is an energy evoking, and directing, agent. Symbolism that is something that stands for another, it can be place, object, or a person. Human cultures use symbols to express specific ideologies and social structures and to represent
“For just as the body is one and has many members, and all the members
Symbol: A Symbol is defined as something that represents something else. An example of this can be seen in things that represent us as people. For instance, names is a good example and represents who you are. Also, it should be noted that symbols are arbitrary, since symbols have no necessary connection to what they represent.
These statements assert that the negative ( or contradictory) of an alternative proposition is a conjunction which the conjuncts are the contradictions of the corresponding alternants. That the negative of a conjunctive is an alternative proposition in which the alternants are the contradictories of the corresponding conjuncts.
o Things can only have “right names” only if there is a necessary connection between symbols and things being symbolized.
"Symbolic Meanings Blog for Whats-Your-Sign.com." Symbolic Meanings Blog by Avia Venefica RSS. N.p., n.d. Web. 9 Jan. 2014. .
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
...t the object is an actual constituent of that proposition. The proposition contains merely the constituents of those words contained in the denoting phrase.
learn what a symbol is. A symbol cannot be seen as a sign. The two are
Logic, as it appears in its everyday form, seems to stand on its own, without any requirements to needed to justify its existence. However, it is commonly overlooked that "logic is the science and means of clear . . . communication." Consequently, many sentences are regarded as logical, which in reality are illogical. It can therefore be found that the language used to communicate this logic must be carefully constructed using a certain format in order to form a logical statement. The requirements in such a sentence include a subject, the verb "to be", a predicate containing information that is relevant to the subject by means of the verb "to be", an adjective, and it must have correct reference numbers. Therefore, logic must consist of sentences of a certain kind, in order to be formatted with the intention of revealing or displaying something. It is because of the former items that a logical sentence cannot exist unless it contains all of the previously mentioned grammatical parts.
The sentence “all cats are black” is evidently untrue even if only one cat in the whole universe were to be white. Thus, the property “being black” cannot form a part of the definition of a cat. The lesson to be learnt is that definitions must be universal. They must apply to all the members of a defined set (the set of “all cats” in our example).
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.