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11. If for some natural numbers a and 1. Gertanin i then which of the following to not true? and bare relatively prime LCM(a,b)=ab C a/b=0.5 then a can be 1 and bean be 2 If a/b=0.6 then a can be 6 and b can be 10 14. Whichone of the following is not true? The set of integers is closed under subtraction. Every even number is composite. Every integer has an additive inverse. Multiplication is commutative on the set of natural numbers 15. Consider the statement. P(n):1+2+2^2+ldots +2^n=2^n+1-1 for nin N To prove this statement using the principle of Mathematical induction what would the inductive hypothesis P(k) be? It is true for n=1 1+2+2^2+ldots +2^k=2^k-1-1 1+2+2^2+ldots +2^n+2^n+1=2^n+2-1 1+2+2^2+ldots +2^k=2^k+1-1 16. Which one of the following is a false statement? The set of rational numbers is closed under addition. The sum of any two irrational numbers is irrational. Any non-empty subset of natural numbers has the least element. Any non-empty subset of real numbers has the least upper bound and greatest lower bound. 17. Which one of the following is not a rational number between (1)/(3) and (1)/(2) (5)/(12) (11)/(24) O (3)/(8) (1)/(2)

Pergunta

11. If for some natural numbers a and
1. Gertanin i
then which of the following
to not true?
and bare relatively prime
LCM(a,b)=ab
C a/b=0.5
then a can be 1 and bean be 2
If a/b=0.6
then a can be 6 and b can be 10
14. Whichone of the following is not true?
The set of integers is closed under subtraction.
Every even number is composite.
Every integer has an additive inverse.
Multiplication is commutative on the set of natural numbers
15. Consider the statement.
P(n):1+2+2^2+ldots +2^n=2^n+1-1 for nin N
To prove this statement using the principle of Mathematical induction what would
the inductive hypothesis P(k) be?
It is true for n=1
1+2+2^2+ldots +2^k=2^k-1-1
1+2+2^2+ldots +2^n+2^n+1=2^n+2-1
1+2+2^2+ldots +2^k=2^k+1-1
16. Which one of the following is a false statement?
The set of rational numbers is closed under addition.
The sum of any two irrational numbers is irrational.
Any non-empty subset of natural numbers has the least element.
Any non-empty subset of real numbers has the least upper bound and
greatest lower bound.
17. Which one of the following is not a rational number between (1)/(3) and (1)/(2)
(5)/(12)
(11)/(24) O
(3)/(8)
(1)/(2)

11. If for some natural numbers a and 1. Gertanin i then which of the following to not true? and bare relatively prime LCM(a,b)=ab C a/b=0.5 then a can be 1 and bean be 2 If a/b=0.6 then a can be 6 and b can be 10 14. Whichone of the following is not true? The set of integers is closed under subtraction. Every even number is composite. Every integer has an additive inverse. Multiplication is commutative on the set of natural numbers 15. Consider the statement. P(n):1+2+2^2+ldots +2^n=2^n+1-1 for nin N To prove this statement using the principle of Mathematical induction what would the inductive hypothesis P(k) be? It is true for n=1 1+2+2^2+ldots +2^k=2^k-1-1 1+2+2^2+ldots +2^n+2^n+1=2^n+2-1 1+2+2^2+ldots +2^k=2^k+1-1 16. Which one of the following is a false statement? The set of rational numbers is closed under addition. The sum of any two irrational numbers is irrational. Any non-empty subset of natural numbers has the least element. Any non-empty subset of real numbers has the least upper bound and greatest lower bound. 17. Which one of the following is not a rational number between (1)/(3) and (1)/(2) (5)/(12) (11)/(24) O (3)/(8) (1)/(2)

Solução

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KawanEspecialista · Tutor por 3 anos

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Let's go through each question one by one:

1. The statement "LCM(a,b)=ab" is not true when a and b are relatively prime. In this case, the LCM(a,b) is simply the product of a and b.

2. If a/b = 0.5, then a can be any number that is half of b. For example, if b = 10, then a can be.

3. The statement "Every even number is composite" is not true. For example, the number 2 is an even number but it is not a composite number.

4. The statement "Multiplication is commutative on the set of natural numbers" is not true. For example, 2 * 3 is not equal to 3 * 2.

5. To prove the statement P(n): 1+2+2^2+...+2^n = 2^(n+1) - 1 using mathematical induction, the inductive hypothesis would be P(k): 1+2+2^2+...+2^k = 2^(k+1) - 1.

6. The statement "The sum of any two irrational numbers is irrational" is not true. For example, the sum of √2 and -√2 is 0, which is a rational number.

7. The number 1/2 is not a rational number between 1/3 and 1/2.
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