I'm doing math through correspondence so material is not explained very well. I would appreciate if someone could explain this to me. This lesson is review of set theory and first degree equations.
Indicate whether each of the following statements is true or false. If the statement is false, explain why it is false.
a) 3/4EQ
b) the square root -31 ER
c) 0EI
d) -2EW
The four are neither statements nor equations. You are also falsely assuming that we know what the E acronyms are.
That is what the question states although the E is like one of those mathematical E i thought they stood for all real numbers but im not sure
To determine whether each statement is true or false, we need to understand the meaning of the symbols used.
a) 3/4EQ:
To interpret this statement, we need to understand the meaning of the symbols involved.
- The symbol "/" typically represents division.
- The symbol "E" usually denotes the concept of "belongs to" or "is an element of."
- The symbol "Q" represents the set of rational numbers.
Based on this information, we can break down the statement as follows:
"3/4 belongs to the set of rational numbers."
This statement is true because any number that can be expressed as a ratio of two integers (which 3/4 can) is considered a rational number.
b) The square root -31 ER:
Similarly, we need to understand the meaning of the symbols used.
- The phrase "square root" usually represents the principal square root.
- The symbol "-" indicates a negative number.
- The symbol "E" denotes the concept of "belongs to" or "is an element of."
- The symbol "R" represents the set of real numbers.
Breaking down the statement:
"The principal square root of -31 belongs to the set of real numbers."
This statement is false because the square root of a negative number is not a real number. If this statement were true, it would imply that the principal square root of a negative number exists in the set of real numbers, which is not the case. Instead, the square root of a negative number is considered a complex number.
c) 0EI:
- The number 0 is a specific value.
- The symbol "E" denotes the concept of "belongs to" or "is an element of."
- The symbol "I" usually represents the set of integers.
Based on this information, we can break down the statement as follows:
"0 belongs to the set of integers."
This statement is true because 0 is an integer.
d) -2EW:
- The number -2 is a specific value.
- The symbol "E" denotes the concept of "belongs to" or "is an element of."
- The symbol "W" represents the set of whole numbers.
Breaking down the statement:
"-2 belongs to the set of whole numbers."
This statement is false because -2 is an integer but not a whole number. Whole numbers include continuous positive integers starting from zero (0, 1, 2, 3, ...), while integers include both positive and negative whole numbers and zero (-2, -1, 0, 1, 2, ...). Therefore, -2 does not belong to the set of whole numbers.
By understanding the concepts and symbols being used, we can determine the truth or falsity of each statement.