if p and q are two propositions,use truth table technique to show that a) (p=q) ^ (q=p)= p=q and b) [(p=q) ^ p]=q is a Tautology​

Answers

Answer 1

Answer:

  see attached

Step-by-step explanation:

The truth table technique shows the first proposition is True. However, the second proposition cannot be shown to be a tautology, because it isn't true.

__

a.

The "equals" relation is commutative: (a=b) ≡ (b=a), hence the expression ...

  (p=q)∧(q=p)

is equivalent to

  (p=q)∧(p=q)

We know that the And of p with itself is just p, so that fact ensures the truth of ...

  (p=q)∧(p=q) = (p=q)

Hence

  (p=q)∧(q=p) = (p=q)

The top truth table in the attached shows the final comparison of the two expressions is true for all values of p and q.

__

b.

The attached truth table shows that the given relation is not a tautology.

If P And Q Are Two Propositions,use Truth Table Technique To Show That A) (p=q) ^ (q=p)= P=q And B) [(p=q)

Related Questions

help me out guys thank u

Answers

Answer:

[tex] \sf \: a5 = 769[/tex]

Please help in stuck on this one

Answers

Answer:

Step-by-step explanation:

a.

[tex]2^3*2^{-3}=2^0\\b.\\\frac{2^3}{2^5} =2^{-2}\\c.\\2^{-3}*5^{-3}=10^{-3}[/tex]

Dante is saving money to buy a game. So far he has saved $24, which is two-thirds of the total cost of the game. How much does the game cost?

Answers

Answer:

The game costs 36$ dollars.

Step-by-step explanation:

2/3 of 36 is 24 :p

The total cost of the game Dante wants to buy is 26 dollars.

What is a fraction?

A fraction describes some parts of a certain quantity. Fractions are of two types one is a proper fraction and another is an improper fraction. In a proper fraction, the numerator is smaller than the denominator and n improper fraction numerator is greater than the denominator.

Assuming The total cost of the game is x dollars.

Given that 24 dollars is (2/3)rd of the total cost of the game.

So we can write 24 is (2/3)rd of the total cost of the game.

∴ 24 = (2/3)×x.

24 = (2/3)x.

x = 24×(3/2).

x = 12×3.

x = 36 dollars.

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is 5/74 rational or irrational?

Answers

Answer:

Rational

Step-by-step explanation:

5.74 is the same as 5.74 over 1. In other words, 5.74 can be written with a numerator and denominator, like this:

 5.74  =  5.74/1

   

5.74 x 100/ 1 x 100

You can multiply the numerator and denominator of any fraction by the same number and keep the value of the fraction the same. Here we will multiply the numerator and denominator by 100 to get rid of the decimal point.

   

5.74 × 100/ 1 × 100

When we calculate the numerator and the denominator above, we get this fraction:

   

574/100

The fraction above is the same as 5.74. Furthermore, the numerator and the denominator of the fraction above are integers. Therefore, we can conclude that the answer to "Is 5.74 a rational number?" is yes.

Rational. Any fraction is a rational number is the numerator and denominator are integers.

please help me out, simple

Answers

Answer: 45°

Reason: since the angle adjacent to ATC is 90° we can assume that ATC = 90°. Since ATB is 45° we can subtract this from ATC to get us 45° for BTC.

Answer:

Answer is 45⁰

Step-by-step explanation:

The angle ATB IS 45⁰

15 over r - 1 when r= 5

Answers

plug in 1 for r so (-1 + 5) = 4
15 / 4 = 3.75

what is the unit rate of 36 ounces of 5.79

Answers

A unit ounce is 0.16

If 36 ounces worth 5.79, 1 ounce will be

= 5.79 / 36

= 0.1608

Which statement correctly explains the difference between a right cylinder and an elliptic cylinder?
A right cylinder has circular bases while an elliptic cylinder has oval bases.
A right cylinder has rectangular bases while an elliptic cylinder has oval bases.
A right cylinder has triangular bases while an elliptic cylinder has oval bases.
A right cylinder has rectangular bases while an elliptic cylinder has circular bases.

Answers

If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder. If the bases are disks (regions whose boundary is a circle) the cylinder is called a circular cylinder

Find the value of cos F rounded to the nearest hundredth, if necessary

Answers

Using the trigonometric ratios, the value of cos F in the right angle triangle is 0.28 .

What are right angle triangle?

Right angle triangle are triangle that has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore,

cos F = adjacent / hypotenuse

adjacent = FE

hypotenuse = 50

50² - 48² = FE²

FE = √2500 - 2304

FE = √196

FE = 14

Therefore,

cos F = 14 / 50

cos F = 0.28

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Which of the following are not polynomials?

Answers

Answer:

D

I really wish is right!!!

HELP, i need help!!!!!!!!!!!!!!

Answers

Answer:

t = 7.46, 0.42

Explanation:

h = 126t - 16t²    [ "h" is height, "t" is time ]

when height is 50 feet

126t - 16t² = 50-16t² +126t -50 = 016t² -126t +50 = 0

==================

[tex]\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]

==================

[tex]\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}[/tex]

[tex]\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}[/tex]

[tex]\Longrightarrow \sf t = 7.46, \ 0.42[/tex]

Let's find

h=126t-16t²

Put h=50

-16t²+126t=50-16t²+126t-50=0

Use quadratic formula

[tex]\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}[/tex]

[tex]\\ \rm\Rrightarrow t=7.5s,0.4s[/tex]

Write the exponential function y = 22(1.35)' in the form y = aekt.
(a) Once you have rewritten the formula, give k accurate to at least four decimal places.
k%3D
help (numbers)
If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual and
continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing
decay the negative rate is implied).
(b) The annual? rate is
% per year (round to the nearest 0.01%).

Answers

Answer:

y = 22·e^(0.3001t), growingannual rate: 35%continuous rate: 30.01%

Step-by-step explanation:

When an exponential function is in the form ...

  y = ab^t

the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...

  b = 1 +r

In the alternate form, this can be written ...

  y = a·e^(kt)

Comparing the forms, we see that ...

  b = e^k   ⇒   k = ln(b)

__

(a)

  y = 22·1.35^t

  k = ln(1.35) ≈ 0.3001

  y = 22·e^(0.3001t)

The growth factor is greater than 1, so the function is growing.

__

(b)

The annual growth rate is ...

  r = 1.35 -1 = 0.35 = 35.00%

__

(c)

The continuous growth rate is ...

  k = 0.3001 = 30.01%

At noon, there are 700 juniors and 1,100 seniors at a college fair. After 12:00 p.m., 20 juniors arrive every 15 minutes and 45 seniors leave every 15 minutes. What is the ratio of juniors to seniors at 2:00pm in fraction form

Answers

Answer:

find the common factor in the given algebraic expressions 4 (x-y) , 6(y-x)

Find the slope of the line passing through the points (7, -3) and (3, -7)

Answers

Answer:

The slope of the line is -1

Step-by-step explanation:

You need to use the slope formula

Slope Formula: y2 - y1 / x2 - x1

**The numbers represent subscripts but the subscripts aren't on computers**

Your Coordinate Points:

(7, -3) and (3, -7)

Do -7 - (-3) / 3-7

First, do -7 - (-3)

The negatives cancel to an addition problem.

-7 + 3

Now do -7 + 3. This is a subtraction problem that should be negative.

-7 + 3 = -4

Next, do 3 - 7

That should be 4

-4/4 is what we have right now.

Do -4 divided by 4 which has to contain a negative.

That is simply -1.

The slope of the line is -1

All the clocks below show the time in the aftemoon or evening. Write the times below the clocks using 24 hour time. Time is Time is Times Times​

Answers

Answer:

1. 15:00

2. 20:10

3. 14:20

4. 14:45

5. 17:45

Step-by-step explanation:

Susan has 600 feet of fencing to use in making a yard for her new puppy. The yard she has
planned has a length that is 75 feet less than twice the width. What are the dimensions of the
yard?

Answers

Answer:

Length = 175

Width = 125

Step-by-step explanation:

P=2(L+W)

600ft=2(L+W)

300=L+W

300=2W-75ft+W

375=3W

125=W

L=2W-75

L=2(125)-75

L=250-75

L=175

Lainey is sliding down a water slide that is 423 feet long at a rate of 47 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?

Answers

Answer:

It will take Lainey 9 seconds to travel from top to bottom

Further explanation:

The formula of speed will be used to calculate the time to reach from top to bottom of the slide.

Given

\begin{gathered}Distance=d=423\ feet\\Speed=s=47\ feet\ per\ second\end{gathered}

Distance=d=423 feet

Speed=s=47 feet per second

The formula for speed is:

s=\frac{d}{t}s=

t

d

Putting the values of distance and speed in the formula:

\begin{gathered}47=\frac{423}{t}\\t=\frac{423}{47}\\t=9\ seconds\end{gathered}

47=

t

423

t=

47

423

t=9 seconds

It will take Lainey 9 seconds to travel from top to bottom

Keywords: Speed, distance

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Please Help!!!!!!!! In a recent year,24.7% of all registered doctors were female. If there were 43,200 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.

Answers

Answer:   174,899

This is one single number just a bit under 175 thousand. Delete the comma if needed.

========================================================

Work Shown:

x = number of total doctors

24.7% of x = number of female doctors

0.247x = 43200

x = 43200/(0.247)

x = 174,898.785425101 approximately

x = 174,899 when rounding to the nearest whole number

Find the hourly wage for a person with an income of $60376, who works 57 hours a week for 44 weeks.

Answers

Answer:

$24.07

Step-by-step explanation:

57×44=2508 hrs

60376÷2508=$24.07 per hr

please help, super easy 7th grade math! worth a lot of points

Answers

Answer:

57mm

Step-by-step explanation:

Length of missing side= perimeter- known lengths

= 152mm- (30+20+45)mm

= (152 - 95)mm

= 57mm

You must take the total perimeter and subtract what you know to find the missing side. So 152-30-20-35= 57

A person who can afford a monthly payment of __________ and signed a mortgage with a monthly payment of __________ was most likely the victim of predatory lending.

A. $900; $1000
B. $900; $800
C. $900; $900
D. $900; $700

Answers

Answer:

A . 900-1000

Step-by-step explanation:

Given the sequence 1,1,2,3,5,8….,find the 6th term

Answers

Answer:

8 is the ans because it is 8

I hope I can help you

Find the distance between the two points in simplest radical form.
(-8,3) and (-2,5)

Answers

Explaination :

Here we would be using distance formula to calculate the distance between those two points.

Points are,

(-8,3) (-2,5)

Distance Formula :

[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]

We have :

x1 = -8 x2 = -2 y1 = 3 y2 = -5

Substituting the values :

Refer the attachment.Additional Information :

Centroid of a triangle :-

[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]

Midpoint of two points:-

[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]

9. Find the value of x. Round your answer to the nearest tenth.
sin Xº = 4/15

Answers

Answer: 15.5 degree

Step-by-step explanation:

NEED HELP ASAP!!!
On a coordinate plane, sketch the graphs. y=|x| , y=|x+3| , and y=|x-2|

Answers

Answer:

Step 1. Plot x-intercept

Step 2. Plot y-intercept

Step 3. Connect dots

y = |x|

x-intercept = (0,0)

y-intecept = (0,0)

y = |x + 3|

x-intercept = (-3,0)

y-intecept = (0,3)

y = |x - 2|

x-intercept = (2,0)

y-intecept = (0,2)

BRAINLIEST please if this helped!

Mrs. Angle has 12 students in her advanced algebra class. On a recent test, the average was 80. When Beth asked for her score, Mrs Angle could not find it, but she did remember adding Beth's score in the average. She also remembered Beth had passed. These are the scores of the other students

65, 65, 70, 70, 80, 85, 90, 90, 90,100.

What is Beth's score?

Answers

Answer:

75

Step-by-step explanation:

Let the Beth's score is x.

The average is 80.

Solve the following equation:

average = sum / number(65*2 + 70*2 + 80 + 85 + 90*3 + 100 + x)/11 = 80805 + x = 80*11x = 880 - 805x = 75

Beth's score was 75

[80 POINTS] An engineer is designing a new drill bit as shown in the diagram. To finalize the design, the engineer needs to know the volume of the drill bit.
What is the volume of the drill bit?

Answers

Answer:

2,106 pi mm3

Step-by-step explanation:

Volume of the drill bit is equals to [tex]2,106\pi mm^{3}[/tex].

What is volume?

" Volume is defined as the total space occupied by a three dimensional object enclosed in it. It is measured in cubic unit."

Formula used

Volume of the cone =  [tex]\frac{1}{3} \pi r^{2}h[/tex]

Volume of the cylinder =[tex]\pi r^{2}h[/tex]

r = radius of the cone / cylinder

h = height of the cone / cylinder

According to the question,

Given,

Radius of the cylinder = 9 mm

Radius of the cone = 9 mm

Height of the cone = 24 mm

Height of the cylinder = 18 mm

Substitute the values in the formula to obtained the required volume,

Volume of the cone [tex]= \frac{1}{3} \pi (9^{2})(24)[/tex]

                                 [tex]= \pi (81)(8)\\=648\pi mm^{3}[/tex]

Volume of the cylinder [tex]= \pi (9^{2} )(18)[/tex]

                                       [tex]=1458\pi mm^{3}[/tex]

Required Volume of the drill pit

= Volume of the cone + Volume of the cylinder

[tex]= (648\pi + 1458\pi )mm^{3} \\= 2106\pi mm^{3}[/tex]

Hence, Option(B) is the correct answer.

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end
A cruise ship is 1480 feet from a light house off a Caribbean Island.
If the angle of elevation from the cruise ship to the top of the light
house is 4º, what is the height of the lighthouse? Round to the
nearest whole foot.

Answers

Answer:

104 feet

Step-by-step explanation:

To get the height of the lighthouse, we need to take the sine function of the anglesin4° = 0.07sin4° = h/1480⇒ h/1480 = 0.07⇒ h = 1480 x 0.07⇒ h = 103.6⇒ h = 104 feet

CAN SOMEONE PLS ANSWER THIS QUESTION FAST
I WILL MARK BRAINLIEST

Answers

Answer:

B 5

Step-by-step explanation:

it is the same ratio as the red

The sum of squares of lengths of the two sides of a rectangular field is 25m2.Their difference is 1m .what is the length of each side of the field

Answers

Answer:

Perimeter of a rectangle = 2×(Length+Breadth)

(i) Length = 16.8 cm

Breadth = 6.2 cm

Perimeter = 2×(Length+Breadth)

= 2×(16.8+6.2) =46 cm

(ii) Length = 2 m 25 cm

=(200+25) cm (1 m = 100 cm )

= 225 cm

Breadth =1 m 50 cm

= (100+50) cm (1 m = 100 cm )

= 150 cm

Perimeter = 2×(Length+Breadth)

= 2×(225+150) =750 cm

(iii) Length = 8 m 5 dm

= (80+5) dm (1 m = 10 dm )

= 85 dm

Breadth = 6 m 8 dm

= (60+8) dm (1 m = 10 dm )

= 68 dm

Perimeter = 2×(Length+Breadth)

= 2×(85+68) =306

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