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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.

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Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.

Juliette [100K]

Answer:

see below for the tables

Step-by-step explanation:

The differential equation is separable, so the solution is ...

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4 0

3 years ago

Is this correct please

Katen [24]

18a is correct, 18b is incorrect, 18c is correct, 18d is false, 18e is false, 18f is true, 19 is incorrect.

6 0

3 years ago

a local businesses bought a square ploy of land. the sides of the lot measure 32 feet on each side. he decides to split the lot

san4es73 [151]

Answer:

Approximate length of the diagonal fencing needed is 45.25 cm.

Step-by-step explanation:

Here, each side of the square shaped land = 32 ft

Now, the diagonal fencing is made in side the plot so that the land is divided into two right triangles.

In the triangle:

Base side of the triangle = 32 cm

Perpendicular length of the triangle = 32 cm

Let us assume the hypotenuse of the triangle = k cm

⇒The length of the diagonal in the square = k cm

by PYTHAGORAS THEOREM in a right angled triangle:

$(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}$

⇒ $(32)^2 + (32)^2 =k^2\\or, k^2 = 1024 + 1024 = 2048\\\implies k = \sqrt{2048} = 45.25$

or, k = 45.25 cm

Hence,the approximate length of the diagonal fencing needed to fence the square land is 45.25 cm.

6 0

3 years ago

Three friends each have some ribbon. Carol has 54 inches of ribbon, Tino has 7.5 feet of ribbon, and Baxter has 3.5 yards of rib

Nastasia [14]

1 ft = 12 inches......1 yd = 36 inches

carol has 54 inches
Tino has 7.5 ft......7.5 * 12 = 90 inches
baxter has 3.5 yds......3.5 * 36 = 126 inches
for a total of : (54 + 90 + 126) = 270 inches total <===

1 ft = 12 inches....so 270 inches = 270/12 = 22.5 ft <==
1 yd = 36 inches..so 270 inches = 270/36 = 7.5 yds <==

5 0

3 years ago

Match the functions to the ranges when the domain is (1,2) ...f(x)=3x + 5 F(x) = x^2 - 2x -5 F(x) =(x+5)x^2 F(x) =4-x

Mice21 [21]

Dommain is input
range is output from given input (domain)

1,2
just input 1 for x and evaluate
then input 2 for x and evaluate

f(x)=3x
f(1)=3(1)=3
f(2)=3(2)=6
range=(3,6)

f(x)=x^2-2x-5
f(1)=1^2-2(1)-5=1-2-5=-6
f(2)=2^2-2(2)-5=-5
range=(-6,-5)

f(x)=(x+5)x^2
f(1)=(1+5)(1^2)=(6)(1)=6
f(2)=(2+5)(2^2)=(7)(4)=28
range=(6,28)

f(x)=4-x
f(1)=4-1=3
f(2)=4-2=2
range=(3,2)

4 0

3 years ago

Read 2 more answers