Determine if the following statement is true or false. (Enter TRUE if the statement is true, enter a counterexample if the statement is false).If m and n are any positive integers and mn is a perfect square, then m and n are perfect squares.

The answer is: the satement is FALSE.  

Step-by-step explanation:

The first step is to transform the propositons in the statement into symbols:

A: m is any positive integer

B: n is any positive integer

C: mn is a a perfect square

D: m is a perfect square

E: n is a perfect square

After that we replace the symbols into the statement:

If A and B and C, then D and E

Logical connectives on the satement are:

So now, we are going to replace the logical connectives on the statement:

((A ∧ B) ∧ C)  ⇒ (D ∧ E)

There is a hierarchy in logical connectives, first we evaluate those inside brackets. The principal connective is evaluated at the end. In this particular case, the principal connective is the conditional.

As we have five different propositions, the combinations are given by the following rule:

2^n= 2^5=32

32 different combinations  

In figure 1, added bellow, it shows the construction of truth table.

In figure 2, added bellow, it shows the development of the truth table. In the development, we don't have as a result a tautology, therefore the statement is FALSE.  

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40

false

step-by-step explanation:

the meaning of changing is to edit or make something different.

but transmitting means cause (something) to pass on from one place or person to another.

there 2 different things