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TiliK225 [7]
2 years ago
6

Use the rules of inference to prove the conclusion r given (all 1,2,3 and 4) the four premises listed below. Write your solution

as a numbered sequence of statements. Identify each statement as either a premise, or a conclusion that follows according to a rule of inference from previous statements, or it is equivalent to a previous statement by the rules of logical equivalences. You should give the rule used by name and refer by number to the previous statement(s) that the rule was applied to.
a. p +- (premise)
b. p Vu (premise)
c. q (premise)
d. ((r Λ t) V p) V-u (premise)
Mathematics
1 answer:
aniked [119]2 years ago
3 0

Answer:

attached below

Step-by-step explanation:

Applying the rule of logical equivalences

attached below  is a detailed solution ( written as a numbered sequence of statements )

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A group of friends went out for dinner and decided to split the cost of the bill equally. If each person contributed $32, the fr
lianna [129]

Answer:

The number of friends that went out for dinner is 8

And their bill is $238

Step-by-step explanation:

Let's assume that the number of friends that went out for dinner to be x

And the bill for the dinner to be y

If each person contributed $32 and paid off the bill,they will have a balance of $18

32x - 18 = y_____equation 1

If each person contributed $35 and paid off the bill and also 15% tip,they will have a balance of $6.30

35x - 6.3 = y + (15% of y)

35x - 6.3 = y + (3y/20)

Open up the bracket

35x - 6.3 =(20y + 3y)/20

700x - 126 = 23y______equation 2

From equation 1,y = 32x - 18

Put the above in equation 2 and we have

700x - 126 = 23(32x -18)

700x - 126 = 736x - 414

collect like terms

36x = 288

x = 288/36

x = 8

Remember that equation 1 says that y = 32x - 18 and we now know that x = 8 .

Substitute and we have

(32 × 8) - 18

y = 238

The number of friends that went out for dinner is 8

And their bill is $238

3 0
3 years ago
Ravi sold 1/5 of his apples. He gave his friend 2/5 of the remainder. Ravi remained with 60. How many apples did ravi have at fi
zheka24 [161]

Answer:

The number of Apples did Ravi have at first is 125 .

Step-by-step explanation:

Let the number of Apples did Ravi have at first = x

The Apples which is sold by Ravi = \frac{1}{5} of x

So, remainder now = x - \frac{1}{5} of x = \frac{4}{5} of x

The apples given to his friend = \frac{2}{5} of \frac{4}{5} x

I.e The apples given to his friend =  \frac{8}{25} of x

Now, The remaining Apples did Ravi have = 50

∴ According to question

\frac{4}{5} of x -  \frac{8}{25} of x = 60

Or,  \frac{20-8}{25} of x = 60

Or,  \frac{12}{25} of x = 60

∴ x = \frac{25\times 60}{12} = 125

Hence The number of Apples did Ravi have at first is 125 .  Answer

8 0
3 years ago
Help show works rep by step I’ll give brainly
masha68 [24]

Answer:

4 lbs left after 5 days

Step-by-step explanation:

First, you need to step up an equation!

You know that Soomin has a total of 20 pounds and that she's using it, so you are going to use subtraction.

She uses 3 1/5 pounds per day so you write:

20 - 3 1/5x

and you know that she wants to know how much she has left after 5 days so you replace the x with 5:

20 - (3 1/5) * 5

Multiply first:

20 - 16

After Subtracting you get the answer:

4 lbs left

8 0
3 years ago
Read 2 more answers
Emily put toys into a square box that is 46 centimeters long. How many square centimeters is the bottom of the box?
Sedaia [141]
If the box is a square and the length of one side is 46cm, then the area of the box in square centimeters is 46 * 46 = 2116.
Final Answer:
d. 2116
Hope I helped :)
7 0
3 years ago
Simplify: cos2x-cos4 all over sin2x + sin 4x
GrogVix [38]

Answer:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

Step-by-step explanation:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}

Apply formula:

\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right) and

\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)

We get:

=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}

=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}

=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}

=\frac{\sin\left(x\right)}{\cos\left(x\right)}

=\tan\left(x\right)

Hence final answer is

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

6 0
3 years ago
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