Tell whether each statement is never, sometimes or always true.
a- An integer is a whole number
b- A whole number is a rational number
c- A rational number is a whole number
A-Sometimes true
B- always true
c- sometimes true
A-Sometimes true
B- always true
c- sometimes true
Its been a while since i've done these and I think this is correct
all correct
Always :)
To determine whether each statement is never, sometimes, or always true, we'll break down the definitions of each term.
a) An integer is a whole number: This statement is always true. An integer is a number that can be positive, negative, or zero, with no fractional or decimal parts. Whole numbers are similarly defined as non-negative numbers with no fractional or decimal parts. Since every integer is a whole number, the statement is always true.
b) A whole number is a rational number: This statement is sometimes true. Whole numbers are a subset of rational numbers since they can be expressed as a fraction with a denominator of 1. However, not all rational numbers are whole numbers. Rational numbers include fractions and decimals that terminate or repeat, such as 1/2 or 0.75. So, while every whole number is a rational number, not every rational number is a whole number.
c) A rational number is a whole number: This statement is sometimes true. As mentioned earlier, rational numbers encompass fractions and decimals that terminate or repeat. Whole numbers are a subset of rational numbers since they can be expressed as fractions with a denominator of 1. However, rational numbers can also include fractions and decimals that extend infinitely without repeating. So, while every whole number is a rational number, not every rational number is a whole number.
In summary:
- Statement a is always true.
- Statement b is sometimes true.
- Statement c is sometimes true.