Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using a direct proof. (a) The product of two rational numbers is a rational number. Solution (b) The quotient of a rational number and a non-zero rational number is a rational number. Solution (c) If x and y are rational numbers then is also a rational number.

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

The product:

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

The quotient:

Express as product

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

The sum:

Take LCM

Proved, because 7/6 is rational

The above proof works for all values of A, B, x and y; as long as they are rational values

The total nom of  code that can be used is equal to 5+3 = 8

The solution is in the following image

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image