Indicate which of the following are true and which are false. for those that are false, change the UPPER-CASE expression to make the statement true.
*Every integer is a WHOLE number
* the quotient of two non zero numbers is always a RATIONAL number
* the counting numbers are subsets of the INTEGERS
1 -5 is an integer but not a whole number.
Perhaps every inter is a POSITIVE OR NEGATIVE WHOLE
2. Replace RATIONAL with REAL
3. Yes, true
since we seem to be dealing with integers, the statement is TRUE if you replace NUMBERS with INTEGERS.
1 false, negative integers are not whole numbers
To determine which statements are true and which are false, let's break it down:
Statement 1: "Every integer is a whole number."
This statement is true. In mathematics, whole numbers include both positive and non-negative integers (0, 1, 2, 3, ...).
Statement 2: "The quotient of two non-zero numbers is always a rational number."
This statement is true. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. Since any division operation can be written as a fraction, the quotient of two non-zero numbers will indeed be a rational number.
Statement 3: "The counting numbers are subsets of the integers."
This statement is true. Counting numbers (also known as natural numbers) start from 1 and continue indefinitely (1, 2, 3, 4, ...). Integers, on the other hand, include both positive and negative numbers along with zero (..., -3, -2, -1, 0, 1, 2, 3, ...). Since all counting numbers are also integers, this statement is true.
Therefore, all three statements are true.