2.Which of the following is an example of closure.
a. The equation 4−6=−2 is an example of the whole numbers being closed under subtraction.
b. The equation 1.5+1.6=3.1 is an example of the rational numbers being closed under addition.
c. The equation 1+0=1 is an example of the natural numbers being closed under addition.********
d. The equation 5−5=0 is an example of the natural numbers being closed under subtraction.
3.Which of the following statements about sets of numbers is true?
a. All integers are rational numbers.
b. All rational numbers are natural numbers.
c. All irrational numbers are integers.******
d. All integers are whole numbers.
can someone plz check my answers that would be much appreciated!
#2 Nope. 0 is not a natural number. B is better
#3 Nope. No irrational number is rational, hence not an integer. You want A.
Your answer for question 2 is correct. The equation 1+0=1 is an example of the natural numbers being closed under addition.
For question 3, your answer is incorrect. The correct statement is: c. All irrational numbers are integers.
Let's analyze each question and answer choice:
2. The question is asking for an example of closure. Closure means that when you perform a certain operation on two elements of a set, the result is also an element of that set.
a. The equation 4−6=−2 is an example of the whole numbers being closed under subtraction. This is incorrect because the whole numbers are not closed under subtraction. Subtracting 6 from 4 results in a negative number, which is not a whole number.
b. The equation 1.5+1.6=3.1 is an example of the rational numbers being closed under addition. This is correct. Adding two rational numbers (1.5 and 1.6) results in another rational number (3.1).
c. The equation 1+0=1 is an example of the natural numbers being closed under addition. This is correct. Adding two natural numbers (1 and 0) always results in another natural number (1).
d. The equation 5−5=0 is an example of the natural numbers being closed under subtraction. This is incorrect because subtracting 5 from 5 results in 0, which is not considered a natural number.
Therefore, the correct answer is option c. The equation 1+0=1 is an example of the natural numbers being closed under addition.
3. The question is asking for a true statement about sets of numbers.
a. All integers are rational numbers. This is true. Every integer can be expressed as a fraction (e.g., 2 can be written as 2/1), and thus, they are all rational numbers.
b. All rational numbers are natural numbers. This is false. Rational numbers include both fractions and decimals, which may or may not be natural numbers.
c. All irrational numbers are integers. This is false. Irrational numbers cannot be expressed as fractions or decimals and do not include integers.
d. All integers are whole numbers. This is true. Integers are whole numbers without any fractional or decimal parts.
Therefore, the correct answer is option c. All irrational numbers are integers.