Final answer:
The statement 'All integers are rational numbers' is true because any integer can be expressed as a fraction with 1 in the denominator. In contrast, the statement 'All rational numbers are integers' is false since rational numbers also include non-integer fractions and decimals.
Step-by-step explanation:
Among the statements given, the true statement is "All integers are rational numbers". This is because any integer can be expressed as a fraction by placing it over 1, which fits the definition of a rational number: a number that can be expressed as a fraction where both the numerator and the denominator are integers, with the denominator not being zero. For example, the integer 5 can be written as 5/1, making it a rational number.
However, the statement that "All rational numbers are integers" is false. Rational numbers include fractions and decimals that can be expressed as fractions, not just whole numbers (integers). An example is 1/2 or 0.5, which is a rational number but not an integer.
Therefore, our understanding of number systems and intuition can support us in recognizing that while all integers are indeed part of the larger set of rational numbers, not all members of the set of rational numbers are integers, due to the inclusion of fractions and non-integer decimals within the rational number set.