Mathematical Statements and Notations: Exercises for University or High School Students, Exercises of Mathematics

Past exercises in Mathematics in Modern World

Typology: Exercises

2022/2023

Uploaded on 04/07/2023

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MATHEMATICAL STATEMENTS
EXERCISES 1:
STATEMENTS CLASSIFICATION TRUE OR FALSE
1. The sum of two real numbers is COMMUTATIVE. ____________ ____________
2. If a real number is multiplied by zero, then
the product is equal to zero . ____________ ____________
3. There exist a real number whose squares is
less than itself. ____________ ____________
4. For all real numbers there exist an ADDITIVE
INVERSE. . ____________ ____________
5. The sum of any two odd numbers is odd. ____________ ____________
6. All perfect squares are even numbers ____________ ____________
7. The INTERSECTION of odd numbers and
NATURAL numbers is an odd number ____________ ____________
8. If two numbers are said to be the factor
of a third number, then any of the two numbers
is a multiple of that third number. ____________ ____________
9. If the product of two numbers is zero then
either of the two number is zero. ____________ ____________
10. There exist a RATIONAL number whose product is
a WHOLE number. ____________ ____________
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MATHEMATICAL STATEMENTS

EXERCISES 1:

STATEMENTS CLASSIFICATION TRUE OR FALSE

  1. The sum of two real numbers is COMMUTATIVE. ____________ ____________
  2. If a real number is multiplied by zero, then the product is equal to zero. ____________ ____________
  3. There exist a real number whose squares is less than itself. ____________ ____________
  4. For all real numbers there exist an ADDITIVE INVERSE.. ____________ ____________
  5. The sum of any two odd numbers is odd. ____________ ____________
  6. All perfect squares are even numbers ____________ ____________
  7. The INTERSECTION of odd numbers and NATURAL numbers is an odd number ____________ ____________
  8. If two numbers are said to be the factor of a third number, then any of the two numbers is a multiple of that third number. ____________ ____________
  9. If the product of two numbers is zero then either of the two number is zero. ____________ ____________
  10. There exist a RATIONAL number whose product is a WHOLE number. ____________ ____________

MATHEMATICAL NOTATIONS, SYMBOLS, OPERATIONS AND VARIABLES

EXERCISES 2:

Translate each of the following MATHEMATICAL STATEMENT/PHRASES into mathematical SYMBOLS.

Use as few variables as possible. Each item may have one or more than one expression/equation.

  1. A number less 8
  2. The square of the sum of 8 and a number
  3. A manโ€™s age 15 years ago
  4. ๐‘ƒ percent of ๐‘ฅ pesos
  5. Two numbers whose sum is 80 and difference is 50
  6. Joe is 2.5 times as old as his brother Ken now. Six years ago, he was four times as old as Ken.
  7. For all real numbers there exist a multiplicative inverse whose product of the number and its multiplicative inverse is 1.
  8. The sum of any two real numbers is real.
  9. If the product of any two number is zero, then either of the two number is equal to zero.
  10. A rational number is defined provided that its denominator is not equal to zero.

Translate the following MATHEMATICAL SYMBOLS to MATHEMATICAL STATEMENTS/PHRASES.

2. (โˆ’2^2 )(๐‘ฅ + ๐‘ฆ)^2

5. โˆ€ ๐‘ฅ โˆˆ ๐‘…| ๐‘ฅ^2 > 0