18 Questions
Which of the following best describes the use of 'and' in Mathematics language?
Addition
In Mathematics, 'is' may have a different meaning from its use in English when it is used to signify:
Equality
Which type of numbers are used for counting in Mathematics?
Cardinal numbers
In Math language, which grouping symbols are commonly used?
Curly brackets
What category does an equation fall under in the language of Mathematics?
Noun
When translating from English to Math language, what do ordinal numbers signify?
Positions
What is the translation of 'Twice a number minus eight' into mathematical expression?
2x - 8
Which phrase translates to the expression 'x/7 = 2'?
The quotient of a number and seven is two
If a set A = {2, 4, 6} and B = {a, b, c}, are they equivalent or equal sets?
Equivalent
What is the product of a number and ten, if the result is eighty?
10x = 80
Which expression represents 'A total of six and some number'?
6 + x
If 'Eight times a number is forty-eight', what is the mathematical expression for this statement?
8x = 48
What is the definition of a proposition?
A statement that is either true or false, but not both
Which term describes a statement that conveys two or more ideas?
Compound statement
In mathematical logic, what does a 'simple proposition' refer to?
A statement with a single idea
What does the vertical line test help determine in mathematics?
Whether a relation is a function or not
Which symbol represents 'and' in mathematical language?
If P represents 'I study hard' and Q represents 'I get good grades', what does the compound proposition 'P and Q' signify?
'I study hard and get good grades'
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
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.
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