All categories

4 years ago

What are the converse, inverse, and contrapositive of the following true conditional? What are the truth values of each?

1 answer:

4 0

In logic, the converse of a conditional statement is the result of reversing its two parts. For example, the statement P → Q, has the converse of Q → P.

For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the converse is 'if a figure is a parallelogram, then it is rectangle.'
As can be seen, the converse statement is not true, hence the truth value of the converse statement is false.

The inverse of a conditional statement is the result of negating both the hypothesis and conclusion of the conditional statement. For example, the inverse of P → Q is ~P → ~Q.
For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the inverse is 'if a figure is not a rectangle, then it is not a parallelogram.'
As can be seen, the inverse statement is not true, hence the truth value of the inverse statement is false.

The contrapositive of a conditional statement is switching the hypothesis and conclusion of the conditional statement and negating both. For example, the contrapositive of P → Q is ~Q → ~P. 
For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the contrapositive is 'if a figure is not a parallelogram, then it is not a rectangle.'
As can be seen, the contrapositive statement is true, hence the truth value of the contrapositive statement is true.

You might be interested in

Write the equation in spherical coordinates. (a) x2 y2 z2 = 64

vekshin1

The equation in spherical coordinates will be a constant, as we are describing a spherical shell.

r(φ, θ) = 8 units.

<h3>How to rewrite the equation in spherical coordinates?</h3>

The equation:

x^2 + y^2 + z^2 = R^2

Defines a sphere of radius R.

Then the equation:

x^2 + y^2 + z^2 = 64

Defines a sphere of radius √64 = 8.

Then we will have that the radius is a constant for any given angle, then we can write r, the radius, as a constant function of θ and φ, the equation will be:

r(φ, θ) = 8 units.

If you want to learn more about spheres, you can read:

brainly.com/question/10171109

8 0

2 years ago

Ray industries bought a touchscreen monitor for $1200 it is expected to depreciate at a rate of 25% per year what was the value

max2010maxim [7]

So for this problem, we will be using the exponential equation format, which is y = ab^x. The a variable is the initial value, and the b variable is the growth/decay.

Since our touchscreen starts off at a value of 1200, that will be our a variable.

Since the touchscreen is decaying in value by 25%, subtract 0.25 (25% in decimal form) from 1 to get 0.75. 0.75 is going to be your b variable.

In this case, time is our independent variable. Since we want to know the value 3 years from now, 3 is the x variable.

Using our info above, we can solve for y, which is the cost after x years.

$y=1200*0.75^3\\y=506$

In context, after 3 years the touchscreen will only be worth $506.

7 0

3 years ago

How to solve x=6y-11 and 3x-2y=-1 by substitution

vagabundo [1.1K]

Substitute x into the second equation:
3(6y-11)-2y=-1
18y-33-2y=-1
16y=32
y=2
Then put the y value into the first equation to get x:
x=6(2)-11
x=1
There you go!

Please mark brainliest

7 0

3 years ago

2) If Michael invests $2000 in the bank at a rate of 5.5% for 6 years how much

Bad White [126]

Answer:

nnn

Step-by-step explanation:

3 0

3 years ago

Rotate this figure 270 degrees clockwise

Lemur [1.5K]

Answer:

it's the third answer

Step-by-step explanation:

360 degrees is a full circle so you subtract the 90 degrees from it and get 270. The only turn it would need to be a full 360 is 90 degrees. hope this helps

6 0

2 years ago

Read 2 more answers