Questions and Answers
Which of the following best describes the use of 'and' in Mathematics language?
In Mathematics, 'is' may have a different meaning from its use in English when it is used to signify:
Which type of numbers are used for counting in Mathematics?
In Math language, which grouping symbols are commonly used?
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What category does an equation fall under in the language of Mathematics?
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When translating from English to Math language, what do ordinal numbers signify?
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What is the translation of 'Twice a number minus eight' into mathematical expression?
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Which phrase translates to the expression 'x/7 = 2'?
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If a set A = {2, 4, 6} and B = {a, b, c}, are they equivalent or equal sets?
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What is the product of a number and ten, if the result is eighty?
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Which expression represents 'A total of six and some number'?
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If 'Eight times a number is forty-eight', what is the mathematical expression for this statement?
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What is the definition of a proposition?
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Which term describes a statement that conveys two or more ideas?
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In mathematical logic, what does a 'simple proposition' refer to?
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What does the vertical line test help determine in mathematics?
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Which symbol represents 'and' in mathematical language?
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If P represents 'I study hard' and Q represents 'I get good grades', what does the compound proposition 'P and Q' signify?
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Study Notes
Nature of Mathematics
- Language of mathematics is a system of conventional spoken, manual (signed), or written symbols that express human thought.
- Mathematics language has its own set of symbols, including English alphabet, numerals, Greek letters, grouping symbols, and special symbols.
Mathematics Language vs. English Language
- Difficulties arise from different meanings or uses of words in math and English, such as "and" equivalent to plus and "is" having different meanings.
- Numbers have different uses in math: cardinal (counting), ordinal (telling positions), and nominal (identifying).
Translation: English to Math Language
- Example translations: y = x, x = y, input-output functions, and function notation.
Functions
- A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
- Vertical Line Test: if a vertical line intersects the graph of a relation at more than one point, then the relation is not a function.
- Examples of functions and non-functions are provided.
Elementary Logic
- Logic serves as a set of rules governing the structure and presentation of mathematical proofs.
- A proposition is a statement that is either true or false, and can be expressed in symbols P, Q, R, or p, q, r.
Sets
- A set in mathematics is a collection of well-defined and distinct objects, considered as an object in its own right.
- Equivalent sets have the same cardinal number, while equal sets have identical elements.
KeyWords to Remember
- equals (=) is, are, was, were, will be, gives, yields, sold for, cost
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Description
Test your knowledge on the language of mathematics, the use of symbols in mathematics, sets, and elementary logic. Explore how mathematics uses a system of symbols to express concepts and ideas.